May/June 2012

If a force $F$ shifts the point where it acts by a displacement $s$ along the direction of the force, the work $W$ done by the force is given by $W = Fs$. How many vector quantities and scalar quantities are present in this equation?

Scalars and vectors

Each option shows a correct word equation that includes force. Which option states the definition of force?

Momentum and Newton's laws of motion

Two identical spheres, each of mass $m$ and speed $v$, are moving directly towards one another. They undergo a head-on elastic collision. Which statement is correct?

Linear momentum and its conservation

The diagram represents a barrel hanging from a frictionless pulley fixed to a building. The rope that supports the barrel passes over the pulley and is tied to a stake at the foot of the building. A man is standing near the stake. The underside of the barrel is $18\,\text{m}$ above the top of the man’s head. The mass of the barrel is $120\,\text{kg}$ and the mass of the man is $80\,\text{kg}$. After untying it from the stake, the man continues to hold the rope and is pulled upwards as the barrel drops. What is the man’s upward speed when his head is level with the bottom of the barrel? (Use $g = 10\,\text{m s}^{-2}$.)

Energy conservation

A cylindrical wooden block has cross-sectional area $A$ and weight $W$. It is completely submerged in water with its axis vertical. The pressures on its top and bottom faces are $p_t$ and $p_b$ respectively. Which expression gives the upthrust on the block?

Density and pressure

A car with mass $m$ moves uphill at steady speed on a slope inclined at an angle $\theta$ to the horizontal, as shown in the diagram. Air resistance and friction create a resistive force $F$. What force is required to drive the car at this steady speed?

Equilibrium of forces

The diagram illustrates a crane holding up a load $L$. A mass is used to supply a balancing load $W$. The load is positioned so that the system is in exact equilibrium, with $Wx = Ly$. The ground exerts a reaction force $R$. The distance $x$ remains unchanged. If the load is shifted further outward so that the distance $y$ increases, and the crane still does not topple, which statement is correct?

Turning effects of forces

A cube made of concrete has side $0.60\,\text{m}$ and a uniform density of $2.0 \times 10^3\,\text{kg m}^{-3}$. It is raised $5.0\,\text{m}$ vertically by a crane. What change in potential energy does the cube have?

Gravitational potential energy and kinetic energy

The resistive force acting against a car’s motion is assumed to vary in proportion to the square of the car’s speed. When the speed is $20\,\text{m s}^{-1}$, the force has a magnitude of $800\,\text{N}$. What effective power must the car’s engine provide in order to keep the car moving at a constant speed of $40\,\text{m s}^{-1}$?

Momentum and Newton's laws of motion

The details below come from a test carried out on a petrol engine in a motor car. Power delivered: $150\,\text{kW}$ Fuel use: $20\,\text{litres per hour}$ Fuel energy content: $40\,\text{MJ per litre}$ Which expression can be used to find the efficiency of the engine?

Energy conservation

What is meant by the internal energy of an object?

Energy conservation

What could be one possible unit for the quantity $VI$, if $V$ is the potential difference across a resistor and $I$ is the current through that same resistor?

Potential difference and power

In each box, the gas molecules are shown as circles, and arrows indicate both the direction of movement and the molecule’s speed. A longer arrow shows a greater speed. Which box contains a gas with the greatest density and the lowest temperature?

Density and pressure

When the temperature is room temperature, the density of liquid mercury is five times greater than the density of solid aluminium. What accounts for this?

Density and pressure

Heating white sugar granules makes them melt. If this melt is then cooled rapidly, a brittle solid toffee forms. What change happens to the structure of the sugar?

Elastic and plastic behaviour

Which property of a metal wire is determined by its Young modulus?

Stress and strain

In the diagram, a wire with diameter $D$ and length $L$ is held tightly at one end between two blocks of wood. A load is then placed on the wire, making it increase in length by $x$. If the same load is applied to a wire of the same material with diameter $2D$ and length $3L$, what extension would it produce?

Stress and strain

What does the gradient of a graph showing force on the vertical axis plotted against extension on the horizontal axis represent?

Elastic and plastic behaviour

Two waves, E and G, are shown. Both waves travel at the same speed. Which statement is correct?

Progressive waves

The diagram presents a displacement-time graph for a progressive wave. What are the wave’s amplitude and frequency?

Progressive waves

Which observation provides evidence that sound waves are longitudinal?

Transverse and longitudinal waves

For a stationary wave to be formed, two waves must move through the same region in opposite directions. Which statement about the properties of these two waves must also be true?

Stationary waves

What would be a sensible estimate for the athlete's average kinetic energy during a $100\ \text{m}$ race lasting $10\ \text{s}$?

Gravitational potential energy and kinetic energy

The wavelength of monochromatic light is determined using a diffraction grating, as the diagram illustrates. The slit separation in the grating is $1.00 \times 10^{-6}\,\text{m}$. The separation between the first-order diffraction maxima is $70.0^{\circ}$. What is the wavelength of the light?

The diffraction grating

A dipole consists of one positive charge and one negative charge with equal magnitude. The electric field pattern for a dipole is illustrated below. At point X, in what direction does the force on an electron act?

Scalars and vectors

A lightning discharge may take place between a charged cloud and the Earth’s surface once the electric field strength in the air between them reaches $25\,\text{kN C}^{-1}$. The diagram illustrates the electric field between the cloud base and the Earth’s surface. What is the least potential difference between the Earth and the base of a cloud, $2\,\text{km}$ high, needed for lightning to occur?

Potential difference and power

A current of $10\,\text{mA}$ flows through a conductor for half an hour. What charge passes a point in the conductor during this interval?

Electric current

An iron wire is $8.0\,\text{m}$ long and its diameter is $0.50\,\text{mm}$. Its resistance is $R$. Another iron wire is $2.0\,\text{m}$ long and has diameter $1.0\,\text{mm}$. What resistance does the second wire have?

Resistance and resistivity

The diagram illustrates a simple circuit. Which statement is correct?

Practical circuits

In the circuit shown below, the ammeter shows $I$ and the voltmeter shows $V$. When the switch is closed, which row states what happens to $I$ and $V$?

Practical circuits

A potential divider is made from a light-dependent resistor (LDR) connected in series with a variable resistor whose resistance is $R$. As the light intensity rises, the resistance of the LDR falls. The variable resistor may be adjusted to either a high resistance or a low resistance. In which arrangement is the output voltage greatest?

Potential dividers

The circuit shown below carries a current $I$ through the resistor $R$. What information must be known to find the value of $I$?

Potential difference and power

A gold foil experiment, in which $\alpha$-particles were scattered, provided new understanding of atomic structure. Which conclusion can be drawn from the results of this experiment?

Atoms, nuclei and radiation

A light-meter measures the intensity $I$ of the light falling on it. Theory indicates that $I$ varies inversely as the square of the distance $d$. Which graph of the results is consistent with this theory?

Progressive waves

Thorium-234 ($^{234}_{90}\text{Th}$) undergoes $\beta$-emission to form a daughter product, which then undergoes another $\beta$-emission to produce a granddaughter product. Which letter in the diagram shows the granddaughter product?

Atoms, nuclei and radiation

During an experiment, a radio-controlled car requires $2.50 \pm 0.05\,\text{s}$ to cover $40.0 \pm 0.1\,\text{m}$. What are the car’s average speed and the uncertainty in this value?

Errors and uncertainties

In an experiment carried out to determine the acceleration of free fall using a falling body, what would cause the value obtained to be too large?

Errors and uncertainties

Which characteristic of a graph makes it possible to determine acceleration?

Equations of motion

The diagram represents a laboratory experiment in which a feather drops from rest inside a long evacuated vertical tube of length $L$. It takes the feather time $T$ to travel from the top of the tube to the bottom. In time $0.50\,T$, how far below the top of the tube will the feather be?

Equations of motion

When air resistance is ignored, a stone is projected from $P$ and moves along a parabolic trajectory, with $T$ as the highest point it attains. The stone passes through $Q$ immediately before it lands. The vertical component of acceleration of the stone is

Equations of motion

How is the unit watt expressed using SI base units?

SI units

A projectile is fired from point $O$ and moves along the trajectory $OPQRS$, as illustrated. Air resistance can be ignored. Which statement is correct about the projectile when it is at the highest point $Q$ of its trajectory?

Equations of motion

Which row correctly indicates whether momentum and kinetic energy are conserved in an inelastic collision when no external forces act?

Linear momentum and its conservation

Two spheres travel towards one another along a single straight line. Before the collision, their speeds are $u_1$ and $u_2$. After the collision, the spheres separate with speeds $v_1$ and $v_2$ in the directions shown below. Which equation has to be true if the collision is perfectly elastic?

Linear momentum and its conservation

A box with mass $8.0\,\text{kg}$ is at rest on a rough horizontal surface. A string is fixed to the box, runs over a smooth pulley, and holds a $2.0\,\text{kg}$ mass on the opposite side. Once the box is let go, a frictional force of $6.0\,\text{N}$ acts on it. What is the acceleration of the box?

Momentum and Newton's laws of motion

A ladder stands on icy (frictionless) ground and is leaning against a rough wall. The moment it is released, it starts to slip. Which diagram correctly indicates the directions of the forces $P$, $W$ and $R$ acting on the ladder as it starts to slide?

Equilibrium of forces

The diagram depicts a solid cube of weight $W$ and side length $L$. It is held on a frictionless spindle that goes through the centres of two opposite vertical faces, one of which is shaded. The spindle is then taken away and fitted again at a position $\frac{L}{4}$ to the right of where it was originally. If the shaded face is being viewed, what torque of the couple must now be applied to prevent the cube from toppling?

Turning effects of forces

A sphere is let go from rest in a viscous fluid. Which graph shows how the acceleration $a$ of the sphere varies with time $t$?

Non-uniform motion

At first, four identical uniform blocks, each with mass $m$ and thickness $h$, lie separately on a table. What work is done on the blocks when they are stacked one on top of another?

Gravitational potential energy and kinetic energy

The diagram illustrates the layout of a water wheel that turns a generator to generate electrical energy. The water has a flow rate of $200\ \text{kg s}^{-1}$. The generator delivers a current of $32\ \text{A}$ at a voltage of $230\ \text{V}$. If any change in the water’s kinetic energy is ignored, what is the efficiency of the system?

Gravitational potential energy and kinetic energy

An engine in a car applies an average force of $500\ \text{N}$ as it moves the car $1.0\ \text{km}$ in $200\ \text{s}$. What is the average power produced by the engine?

Energy conservation

For which quantity is the size a sensible estimate?

Scalars and vectors

A quantity of gas trapped inside a cylinder by a piston is warmed gently. Meanwhile, the piston is adjusted so that the pressure stays constant. Because of this, which change will not happen?

Density and pressure

In an experiment used to demonstrate Brownian motion, a clear container is filled with smoke particles suspended in air. What is observed when the contents of the container are brightly illuminated and examined with a microscope?

Atoms, nuclei and radiation

The diagram illustrates how the atoms are arranged in a certain crystal. Every atom lies at a cube corner. The mass of one atom is $3.5 \times 10^{-25}\ \text{kg}$. The density of the crystal is $9.2 \times 10^{3}\ \text{kg m}^{-3}$. What is the minimum distance between the centres of two neighbouring atoms?

Atoms, nuclei and radiation

A pipe is sealed at one end and contains gas, which is confined by a column of water. The atmospheric pressure is $1.0 \times 10^{5}\ \text{Pa}$. The density of water is $1000\ \text{kg m}^{-3}$. Calculate the pressure of the gas. (Use $g = 10\ \text{m s}^{-2}$.)

Density and pressure

This graph plots force against extension for a wire as it is stretched. To two significant figures, how much work must be done by the tensile force to produce an extension of $7.0\,\text{mm}$?

Elastic and plastic behaviour

A wire extends by $8\,\text{mm}$ when a load of $60\,\text{N}$ is applied. A second wire, made from the same material, has half the diameter and one quarter of the original length of the first wire, and the same load is applied to it. Assuming that Hooke’s law is obeyed, what is the extension of this wire?

Stress and strain

A surveyor’s instrument sends out a laser pulse. How long does the pulse take to travel from the instrument to a wall $150\,\text{m}$ away, bounce off it, and then return to the instrument?

Progressive waves

An electromagnetic wave has a period of $1.0\,\text{ns}$. What are the frequency and wavelength of this wave?

Electromagnetic spectrum

X and Y are two points on the water surface in a ripple tank. A source that produces waves with constant frequency starts to create waves, and these then move past X and Y, making them oscillate. What is the phase difference between X and Y?

Progressive waves

A monochromatic plane wave moving with speed $c$ and wavelength $\lambda$ is diffracted by a small aperture. The diagram shows a succession of wavefronts. How long will it take for some part of the wavefront XY to reach point P?

Diffraction

The diagram shows a vector with magnitude $R$ and perpendicular components $P$ and $Q$. Which row gives the correct description of the perpendicular components?

Scalars and vectors

A standing sound wave is formed between a loudspeaker and a wall. A microphone is linked to a cathode-ray oscilloscope (c.r.o.) and is shifted along a straight line joining the loudspeaker and the wall. The amplitude of the c.r.o. trace increases to a maximum at point X, decreases to a minimum, and then increases again to a maximum at point Y. The separation between X and Y is $33\,\text{cm}$. The speed of sound in air is $330\,\text{m s}^{-1}$. Which diagram shows the c.r.o. trace of the sound detected at X?

Stationary waves

An electric field is present in the region between two charged metal plates. Which graph shows how electric field strength $E$ varies with distance $d$ from $X$ along the line $XY$?

Potential difference and power

At what time does $1\,\text{C}$ of charge pass a point in an electrical circuit?

Electric current

Two copper wires that are equal in length but have different diameters carry the same current. Which statement correctly describes the movement of charged particles through the wires?

Electric current

A power cable $X$ has resistance $R$ and carries current $I$. A second cable $Y$ has resistance $2R$ and carries current $\frac{1}{2}I$. What is the ratio $\dfrac{\text{power dissipated in }Y}{\text{power dissipated in }X}$?

Potential difference and power

The diagram represents a circuit that has four voltmeter readings, $V$, $V_1$, $V_2$ and $V_3$. Which equation connecting the voltmeter readings has to be correct?

Kirchhoff's laws

A battery and a resistor $R$ are connected in series with a light-dependent resistor (LDR). When no light falls on the LDR, its resistance is the same as the resistance of $R$. As the light intensity on the LDR increases, which statement is correct?

Potential dividers

The circuit diagram shows a signal that can display either a green light or a red light. It is operated by the switch $S$. The signal is positioned some distance from $S$ and is linked to it by a cable containing green, red and black wires. At the signal, the green and red wires are attached to the appropriate lamp, while the black wire is joined to terminal $x$ to act as a shared return path. The setup is drawn correctly wired and with the switch in the position that lights the red lamp. While maintenance is being carried out, the wires at the signal are disconnected and then reconnected. On reconnection, the black wire is mistakenly attached to the green lamp (terminal $g$) rather than terminal $x$. The red wire is still connected to its lamp correctly, and the connections at $S$ are unchanged from those shown in the diagram. If the system is then checked with the switch connected to the red wire, what does the signal display?

Practical circuits

Four identical resistors are joined in the three circuit arrangements shown below. Which arrangement gives the greatest total resistance, and which gives the smallest?

Practical circuits

Nuclear decay occurs spontaneously and is random. Which row gives the correct experimental evidence for these two properties?

Atoms, nuclei and radiation

A micrometer screw gauge is used to measure the diameter of a cylindrical metal rod. The diagram gives an enlarged view of the micrometer screw gauge scale when the measurement is being taken. What is the cross-sectional area of the rod?

Errors and uncertainties

Radon $^{222}_{86}\text{Rn}$ starts a decay chain that leads to bismuth $^{214}_{83}\text{Bi}$ by alpha emission and beta emission. When one nucleus of radon decays, how many $\alpha$-particles and $\beta$-particles are emitted?

Atoms, nuclei and radiation

A mass is released from rest and travels a distance of $2.0\,\text{m}$ in a vacuum. An observer measures the time for the mass to move through this distance with a stopwatch operated by hand, then repeats the timing twice more. The mean of the three recorded times is used to find a value for the acceleration of free fall, which is calculated as $9.8\,\text{m s}^{-2}$. The measured times are $0.60\,\text{s}$, $0.73\,\text{s}$ and $0.59\,\text{s}$, giving an average of $0.64\,\text{s}$. Which statement is most appropriate for this experiment?

Errors and uncertainties

The diagram presents two full pulses on the screen of a cathode-ray oscilloscope. A grid made up of $1\,\text{cm}$ squares is drawn across the screen. The time-base setting is $1\,\mu\text{s cm}^{-1}$. How long does each pulse last?

Practical circuits

The graph illustrates how the velocity $v$ of an object travelling along a straight line changes with time from $t = 0$ to $t = T$. Which graph shows the displacement $s$ of the object during the interval $t = 0$ to $t = T$?

Equations of motion

Two markers $M_1$ and $M_2$ are arranged with a vertical separation of $h$. A steel ball is dropped at time zero from a point $x$ above $M_1$. The ball arrives at $M_1$ at time $t_1$ and reaches $M_2$ at time $t_2$. Its acceleration remains constant. Which expression gives the acceleration of the ball?

Equations of motion

A brick becomes detached from a building and drops straight down under gravity. Which graph most accurately shows how its height $h$ above the ground changes with time $t$ when air resistance is ignored?

Equations of motion

What would be a sensible estimate for the average kinetic energy of an athlete while running a $100\,\text{m}$ race lasting $10\,\text{s}$?

Gravitational potential energy and kinetic energy

The diagram depicts a barrel hanging from a frictionless pulley fitted to a building. The rope that supports the barrel passes over the pulley and is fastened to a stake at the foot of the building. A man is standing near the stake. The underside of the barrel is $18\,\text{m}$ above the man’s head. The mass of the barrel is $120\,\text{kg}$ and the mass of the man is $80\,\text{kg}$. After untying the rope from the stake, the man holds onto it and is pulled upwards as the barrel descends. What is the man’s upward speed when his head is level with the bottom of the barrel? (Use $g = 10\,\text{m s}^{-2}$.)

Gravitational potential energy and kinetic energy

Each option presents a correct word equation that includes force. Which option states the definition of force?

Momentum and Newton's laws of motion

Two identical spheres, each of mass $m$ and moving at speed $v$, travel towards one another. They undergo a head-on elastic collision. Which statement is correct?

Linear momentum and its conservation

The diagram illustrates a crane carrying a load $L$. A mass acts as a balancing load $W$. The load is positioned so that the system is exactly in equilibrium, with $Wx = Ly$. The ground exerts a reaction force $R$. The distance $x$ stays unchanged. If the load is moved further away so that the distance $y$ becomes larger and the crane does not topple, which statement is correct?

Turning effects of forces

A wooden cylinder has cross-sectional area $A$ and weight $W$. It is completely submerged in water, with its axis aligned vertically. The pressures acting on its upper and lower faces are $p_t$ and $p_b$ respectively. Which expression is equal to the upthrust on the block?

Density and pressure

A car with mass $m$ moves up a slope at a constant speed, where the slope makes an angle $\theta$ with the horizontal, as illustrated. Air resistance and friction exert a resistive force $F$. What force must be applied to keep the car moving at this constant speed?

Equilibrium of forces

The force opposing the motion of a car is assumed to vary in proportion to the square of the car’s speed. At a speed of $20\,\text{m s}^{-1}$, the force has magnitude $800\,\text{N}$. What effective power must the car’s engine provide to keep the car moving at a constant speed of $40\,\text{m s}^{-1}$?

Energy conservation

A cube made of concrete has side length $0.60\,\text{m}$ and a uniform density of $2.0 \times 10^3\,\text{kg m}^{-3}$. It is raised vertically by a crane through $5.0\,\text{m}$. What change occurs in the cube’s potential energy?

Gravitational potential energy and kinetic energy

What is meant by the internal energy of an object?

Energy conservation

The information shown below comes from a test carried out on a petrol engine in a motor car. power delivered: $150\,\text{kW}$ fuel used per hour: $20\,\text{litres per hour}$ fuel energy content: $40\,\text{MJ per litre}$ Which expression should be used to determine the efficiency of the engine?

Energy conservation

If a force $F$ acts so that its point of application is displaced by $s$ in the same direction as the force, the work $W$ done by the force is given by $W = Fs$. How many vector quantities and how many scalar quantities are represented in this equation?

Scalars and vectors

What does the gradient of a graph with force on the vertical axis and extension on the horizontal axis represent?

Elastic and plastic behaviour

The diagram depicts a wire with diameter $D$ and length $L$, held securely at one end between two pieces of wood. A load is then placed on the wire, making it lengthen by an amount $x$. When the same load is applied to a wire made of the same material but with diameter $2D$ and length $3L$, by what amount will it lengthen?

Stress and strain

Which characteristic of a metal wire is determined by its Young modulus?

Stress and strain

If white sugar granules are heated, they melt. If this molten material is then cooled rapidly, it forms a brittle toffee solid. What change occurs in the structure of the sugar?

Elastic and plastic behaviour

At room temperature, the density of liquid mercury is five times higher than the density of solid aluminium. What accounts for this?

Density and pressure

In each box, identical gas molecules are shown as circles, and arrows indicate the direction of movement and the speed of each molecule. A longer arrow shows a higher speed. Which box contains a gas with the greatest density and the lowest temperature?

Density and pressure

The diagram illustrates a displacement-time graph for a progressive wave. Determine the amplitude and frequency of the wave.

Progressive waves

Two waves E and G are shown. These waves travel at the same speed. Which statement is correct?

Progressive waves

A diffraction grating is being used to determine the wavelength of monochromatic light, as illustrated in the diagram. The slit separation in the grating is $1.00 \times 10^{-6}\,\text{m}$. The angle between the first order diffraction maxima is $70.0^\circ$. What is the wavelength of the light?

The diffraction grating

Which observation demonstrates that sound waves are longitudinal?

Transverse and longitudinal waves

Which unit could be used for the product $VI$, where $V$ represents the potential difference across a resistor and $I$ represents the current through that same resistor?

Potential difference and power

For a stationary wave to form, two waves have to move through the same region in opposite directions. Which statement about the properties of these two waves must also be true?

Stationary waves

A dipole consists of one negative charge and one positive charge with the same magnitude. The dipole's electric field is shown below. In what direction does the force act on an electron at point X?

Electric current

An iron wire is $8.0\,\text{m}$ long and has a diameter of $0.50\,\text{mm}$. Its resistance is $R$. A second iron wire is $2.0\,\text{m}$ long and has a diameter of $1.0\,\text{mm}$. What is the resistance of the second wire?

Resistance and resistivity

A lightning discharge can take place between a charged cloud and the Earth’s surface when the electric field strength in the air between them reaches $25\,\text{kN C}^{-1}$. The diagram illustrates the electric field between the bottom of a cloud and the Earth’s surface. What is the least potential difference between the Earth and the bottom of a cloud, $2\,\text{km}$ above the ground, for lightning to occur?

Potential difference and power

A conductor carries a current of $10\,\text{mA}$ for half an hour. What quantity of charge passes a point in the conductor during this period?

Electric current

In the circuit shown below, the ammeter shows $I$ and the voltmeter shows $V$. After the switch is closed, which row states what happens to $I$ and $V$?

Practical circuits

The diagram illustrates a simple circuit. Which of the following statements is correct?

Practical circuits

In the circuit shown below, a current $I$ flows through the resistor $R$. What information must be known to determine the value of $I$?

Practical circuits

A potential divider is made from a light-dependent resistor (LDR) connected in series with a variable resistor with resistance $R$. As the light intensity rises, the resistance of the LDR falls. The variable resistor may be adjusted to either high resistance or low resistance. In which arrangement is the output voltage greatest?

Practical circuits

Thorium-234 ($^{234}_{90}\text{Th}$) undergoes $\beta$-emission to form a daughter product, which then undergoes further $\beta$-emission to produce a granddaughter product. In the diagram, which letter labels the granddaughter product?

Atoms, nuclei and radiation

During an experiment, a radio-controlled car needs $2.50 \pm 0.05\,\text{s}$ to cover $40.0 \pm 0.1\,\text{m}$. What is the car’s average speed and the uncertainty in this value?

Errors and uncertainties

An experiment in which $\alpha$-particles were deflected by a gold foil led to new understanding of the atom’s structure. Which conclusion can be drawn from the experiment’s results?

Atoms, nuclei and radiation

A light-meter measures the intensity $I$ of the light incident on it. Theory indicates that $I$ varies inversely with the square of the distance $d$. Which graph of the results supports this theory?

Progressive waves

Which characteristic of a graph makes it possible to determine acceleration?

Equations of motion

In an experiment to find the acceleration of free fall using a falling body, what would cause the calculated value to be too large?

Errors and uncertainties

When air resistance is neglected, a stone is launched from point P and moves along a parabolic path, with the greatest height attained at T. The stone arrives at point Q immediately before it lands. The vertical component of the stone’s acceleration is

Equations of motion

The diagram depicts a laboratory experiment in which a feather is released from rest inside a long evacuated vertical tube with length $L$. The feather takes time $T$ to travel from the top of the tube to the bottom. How far below the top of the tube will the feather have travelled in time $0.50T$?

Equations of motion