Oct/Nov 2018

The Earth has a radius of about $6.4 \times 10^6\,\text{m}$, while the Moon has a radius of about $1.7 \times 10^6\,\text{m}$. A student wants to make a scale model of the Solar System in a classroom, with a football of radius $0.12\,\text{m}$ standing for the Earth. Which object would be the most suitable choice to stand for the Moon?

Physical quantities

A charged particle is located in a uniform force field. The force on the particle acts in the direction opposite to that of the field. What is the field, and what is the charge on the particle?

Electric current

A rod that is uniform and $200\ \text{cm}$ long is pivoted freely at point $P$. It remains horizontal in equilibrium because a $60\ \text{N}$ weight is connected to the rod by a string that runs over a frictionless pulley. Determine the weight of the rod.

Turning effects of forces

A ladder is in equilibrium, with one end on rough ground and the other against a rough wall. The ladder’s weight $W$ acts through its centre of gravity $G$. The ladder also experiences forces at $P$ and at $Q$. These forces are $P$ and $Q$ respectively. Which vector triangle shows the forces acting on the ladder?

Equilibrium of forces

A tube that is vertical and sealed at one end is placed in water. Air is trapped in the tube as a column. The density of water is $1000\,\text{kg m}^{-3}$. What is the difference between the pressure of the air in the tube and the atmospheric pressure?

Density and pressure

A rocket is launched vertically. While it speeds up upward after departing the launch pad, which energy forms are being transformed?

Gravitational potential energy and kinetic energy

A mass $m$ rests on a platform, which is held up by gas inside a cylinder of cross-sectional area $A$, as illustrated. The platform has negligible mass and is free to move vertically. The gas is heated and expands, causing the mass to rise by a height $h$. Atmospheric pressure is $p$. What is the ratio $\frac{\text{gain in gravitational potential energy of the mass}}{\text{work done by the gas}}$?

Energy conservation

A weight of $8.00\,\text{N}$ is fastened to the lower end of a spring whose upper end is fixed. Initially, the weight is kept at rest at position X, and the spring is unstretched. The weight is then let go and drops to position Y, which lies $4.00\,\text{cm}$ below X. After oscillating, the weight finally settles at O, which is $2.00\,\text{cm}$ below X. How much energy is lost from the system?

Energy conservation

The force opposing the motion of a car is proportional to the square of the car’s speed. At a speed of $20.0\,\text{m s}^{-1}$, the magnitude of the force is $800\,\text{N}$. What useful output power must be supplied by the car’s engine to keep the car moving at a steady speed of $40.0\,\text{m s}^{-1}$?

Energy conservation

Wires X and Y are made from the same material. Wire Y has twice the diameter and is under twice the tension of wire X. Both wires obey Hooke’s law and start with the same original length. If wire X extends by $e$, what extension does wire Y have?

Stress and strain

What does the gradient of a force (vertical axis) against extension (horizontal axis) graph represent for a wire that obeys Hooke’s law?

Elastic and plastic behaviour

When a beam of light strikes a surface, it transfers energy to that surface. The intensity of the beam is the energy transferred per unit area per unit time. What is the unit of intensity, written in SI base units?

SI units

Forces are exerted on the ends of a rod, causing its length to increase. The graph shows how the rod’s extension $e$ varies with load $L$. Point P marks the elastic limit. Which shaded region shows the work done in the plastic deformation of the rod?

Elastic and plastic behaviour

The graph shows how a quantity $P$ varies with a quantity $Q$ for a sound wave travelling in air. What could $P$ and $Q$ represent?

Transverse and longitudinal waves

A vibration generator creates a progressive wave on a rope. The diagram shows the rope at a particular moment. The wave moves with a speed of $4.0\,\text{m s}^{-1}$. What are the wavelength and frequency for this wave?

Progressive waves

The diagram presents the waveform of a signal on a cathode-ray oscilloscope screen. The time-base is set at $5.0\,\text{ms}$ per division. The Y-gain is set at $5.0\,\text{mV}$ per division. What are the amplitude and the frequency of the signal?

Practical circuits

A jet aircraft moves with speed $0.8v$, where $v$ represents the speed of sound. The aircraft is moving towards an observer at rest. The sound produced by the aircraft has a frequency of $100\,\text{Hz}$. Which frequency is heard by the observer?

Doppler effect for sound waves

A telescope picks up and analyses electromagnetic radiation with wavelength $2\,\text{cm}$. What type of telescope is this?

Electromagnetic spectrum

What can be used to form stationary waves?

Stationary waves

What is one example of wave diffraction?

Diffraction

When light from two lamps shines on a screen, an interference pattern cannot be formed. Why does this happen?

Interference

A beam of light is composed of two wavelengths, $436\,\text{nm}$ and $654\,\text{nm}$. A diffraction grating with $5.00 \times 10^{5}\,\text{lines m}^{-1}$ forms a diffraction pattern in which the second order for one wavelength appears at the identical angle $\theta$ as the third order for the other wavelength. What is the angle $\theta$?

The diffraction grating

A ship moves with a velocity of $8.0\,\text{km h}^{-1}$ in a direction $30^{\circ}$ east of north. What are the east and north components of the ship’s velocity?

Scalars and vectors

Which diagram illustrates the electric field lines around an isolated negative point charge?

Scalars and vectors

An electron beam is sent into an electric field and is bent by the field. Diagram 1 shows an electric field in the plane of the paper. Diagram 2 shows an electric field that is perpendicular to the plane of the paper. The lines A, B, C and D show possible routes for the electron beam. Every route lies in the plane of the paper. Which line most accurately shows the route of the electrons within the field?

Equations of motion

A particle carrying charge $q$ and mass $m$ is initially stationary in a uniform electric field. This field is created by two parallel metal plates a distance $d$ apart and with a potential difference $V$ across them. What is an expression for the acceleration of the charged particle?

Potential difference and power

If a current of $5.0\,\text{A}$ flows through a copper wire, the mean drift speed of the free electrons is $8.0 \times 10^{-4}\,\text{m s}^{-1}$. What is the mean drift speed in another copper wire that has twice the diameter and a current of $10.0\,\text{A}$?

Electric current

What quantity is equal to one volt?

Potential difference and power

The diagram represents a rectangular block with dimensions $x$, $2x$ and $3x$. Electrical contact may be established with the block across opposite pairs of faces (for example, across the faces labelled R). Which statement about the electrical resistance of the block is correct?

Resistance and resistivity

A battery that has internal resistance is joined to a parallel circuit containing two resistors and a switch $S$, as illustrated. At the start, switch $S$ is open. What change is observed in the voltmeter and ammeter readings when switch $S$ is closed?

Practical circuits

A battery is attached to a circuit made up of six resistors, as shown. The potential differences across five of the resistors are marked on the diagram. What is the potential difference across resistor $R$?

Kirchhoff's laws

The diagram depicts a battery with electromotive force (e.m.f.) $6\,\text{V}$, linked in series to a resistor and a uniform resistance wire RQ with a length of $60\,\text{cm}$. The resistance of RQ is the same as that of the resistor. Terminal $X$ is joined to fixed point $R$. Terminal $Y$ is connected to point $P$, and this connection can be made at any point along the wire. $L$ represents the distance from $R$ to $P$. Which graph shows how the potential difference (p.d.) $V$ across $XY$ changes with $L$?

Potential dividers

A nucleus releases a $\beta^-$ particle. How do the proton number and the nucleon number of the nucleus change?

Atoms, nuclei and radiation

A micrometer screw gauge is being used to find the diameter of a copper wire. Diagram 1 shows the reading when the wire is in place. The wire is then taken out and the jaws of the micrometer are closed. Diagram 2 shows the updated reading. What is the diameter of the wire?

Errors and uncertainties

In a nucleus of the nuclide $^{37}_{17}\text{Cl}$, how many up quarks are there, and how many down quarks are there?

Atoms, nuclei and radiation

A digital meter has an accuracy of $\pm 1\%$. It is used to measure the current in an electrical circuit. The meter reading changes between $3.04\ \text{A}$ and $3.08\ \text{A}$. What is the value of the current, with its uncertainty?

Errors and uncertainties

A tennis ball is launched horizontally into the air from the top of a tall building. The effect of air resistance is not negligible. What happens to the ball’s horizontal and vertical velocity components?

Non-uniform motion

Water is pumped along a hose-pipe at a flow rate of $90\ \text{kg}\ \text{per minute}$. It leaves the hose-pipe horizontally at a speed of $20\ \text{m s}^{-1}$. What minimum force must a person apply to the hose-pipe to stop it from moving backwards?

Momentum and Newton's laws of motion

A ball with mass $m$ is projected straight upwards. At the moment the ball’s speed is $v$, the air resistance on the ball has magnitude $F$. What is the magnitude of the ball’s acceleration when its speed is $v$ during its upward motion and during its downward motion?

Momentum and Newton's laws of motion

What does the principle of conservation of momentum state?

Linear momentum and its conservation

A car is moving at a speed of $20\ \text{m s}^{-1}$. The table gives values for the kinetic energy and the momentum of the car. Which pair of values are reasonable estimates?

Momentum and Newton's laws of motion

The diagram illustrates two identical spheres $X$ and $Y$. At the start, $X$ is travelling directly towards $Y$ with speed $v$, while $Y$ is at rest. The spheres undergo an elastic collision. What happens?

Linear momentum and its conservation

As shown, a positively-charged particle of negligible mass moves through a vacuum with constant velocity $v$ and enters the uniform electric field between two parallel plates. After a short time, the particle is at the position indicated. Which diagram shows the force or forces acting on the particle?

Momentum and Newton's laws of motion

A frictionless pivot at its midpoint $P$ holds a uniform rectangular board. Two forces act within the plane of the board. Force $F$ is applied at corner $Q$, while force $2.5F$ is applied at corner $R$. The perpendicular distance from the line of action of force $F$ to point $P$ is $20\,\text{cm}$. The board remains in equilibrium. What is the area of the board?

Turning effects of forces

A kite is balanced while attached to the end of a string, as illustrated. Three forces act on the kite: its weight $W$, the tension $T$ in the string, and the wind force $F$. Which vector diagram shows the forces acting on the kite?

Equilibrium of forces

As the height $h$ above the Earth’s surface gets larger, the density of the air in the atmosphere falls. Which graph most accurately shows how the air pressure $p$ changes with height $h$?

Density and pressure

A bungee jumper standing on a platform above a river is connected to an elastic rope that is $20\,\text{m}$ long when unstretched. He drops towards the river, and at the lowest point he is $30\,\text{m}$ below the platform. As the jumper falls, his initial gravitational potential energy is converted into other forms of energy. Which other forms of energy are present in the jumper and rope when the jumper has fallen half-way, and when he reaches the lowest point of the jump?

Energy conservation

A cylinder holds a fixed mass of gas. With the pressure kept constant at $1.3 \times 10^5\,\text{Pa}$, the gas increases in volume from $900\,\text{cm}^3$ to $1100\,\text{cm}^3$. How much work is done by the gas in this expansion?

Energy conservation

An object is projected upwards into the air. Which graph represents how the object's gravitational potential energy $E_p$ changes with its height $h$ above the ground?

Gravitational potential energy and kinetic energy

A car with mass $1800\,\text{kg}$ moves along a horizontal road, and its speed rises from $20\,\text{m s}^{-1}$ to $25\,\text{m s}^{-1}$ over a time of $5.4\,\text{s}$. What is the average useful power output of the car’s engine?

Gravitational potential energy and kinetic energy

A force that varies in magnitude is applied so that the train is supplied with constant power. Which graph most accurately shows how the applied force $F$ varies with the train's velocity $v$?

Energy conservation

What is the SI base-unit expression for resistance?

Resistance and resistivity

A metal cylinder can sustain a compressive force of $4.0\,\text{kN}$ without undergoing plastic deformation. The cylinder has a cross-sectional area $A$ and reaches its elastic limit when a stress $\sigma$ acts on it. Determine one possible pair of values for $A$ and $\sigma$.

Stress and strain

A wire exhibits both elastic and plastic behaviour. When the load on it is increased gradually, the extension changes with load as indicated by line $OXY$. The load is then removed, as shown by line $YZ$. This results in areas $P$, $Q$ and $R$ being formed on the graph. Which area shows the greatest elastic potential energy stored in the wire?

Elastic and plastic behaviour

A progressive wave travelling along a wire has frequency $10\,\text{Hz}$. Two points on the wire that are $0.25\,\text{m}$ apart show a phase difference of $22.5^\circ$. What is the maximum speed of the wave?

Progressive waves

Plucking a guitar string produces a longitudinal sound wave in the air, as illustrated. The speed of sound in air is $340\,\text{m s}^{-1}$. What is the approximate frequency of the sound wave shown?

Progressive waves

Sound produced by a loudspeaker positioned above a tube makes the air in the tube resonate. A stationary wave is produced with two nodes and two antinodes, as shown. The speed of sound in air is $340\,\text{m s}^{-1}$. What is the frequency of the sound?

Stationary waves

A police car is fitted with a two-tone siren that produces sounds with frequencies of $700\,\text{Hz}$ and $1000\,\text{Hz}$. The car is moving at $40.0\,\text{m s}^{-1}$ towards a stationary observer. The speed of sound in air is $340\,\text{m s}^{-1}$. What is the difference between the two frequencies heard by the observer?

Doppler effect for sound waves

A surveyor’s device sends out a pulse of light. The light reflects off a wall $150\,\text{m}$ away. What is the time taken for the pulse to travel from the device to the wall and then back to the device?

Progressive waves

Progressive sound waves with wavelength $20\,\text{cm}$ are sent into the air columns of a closed pipe $P$ and an open pipe $Q$. The pipe lengths are shown. In which pipe or pipes do stationary waves occur?

Stationary waves

What occurs when waves pass through a gap whose width is equal to their wavelength?

Diffraction

Two microwave sources $P$ and $Q$ emit coherent waves with a phase difference of $180^{\circ}$. These waves share the same wavelength $\lambda$. At point $S$, the interference pattern formed by the two sources has a minimum. The distance $(QS - PS)$ is known as the path difference. In the expressions given, $n$ is an integer. Which expression gives the path difference?

Interference

Which list includes both scalar and vector quantities?

Scalars and vectors

A parallel beam of monochromatic light with wavelength $\lambda$ falls normally on a diffraction grating $G$. As shown, the angle between the directions of the two second-order diffracted beams at $P_1$ and $P_2$ is $\alpha$. What is the grating line spacing?

The diffraction grating

A flat plate carries a positive charge, while a curved plate carries a negative charge. Which diagram shows the electric field lines between these two plates?

Scalars and vectors

As illustrated, two parallel metal plates are linked to a d.c. supply. The plates are then driven towards one another at a constant speed. You may assume that the electric field between the plates is uniform. Point $P$ lies halfway between the plates. Which graph shows how the electric field strength $E$ at point $P$ changes with time $t$?

Potential difference and power

Which two units are involved in defining the coulomb?

Electric current

An electrical device with a fixed resistance of $20\,\Omega$ is placed in series with a variable resistor and a battery whose electromotive force (e.m.f.) is $16\,\text{V}$ and whose internal resistance is negligible. Determine the resistance of the variable resistor when the power dissipated by the electrical device is $4.0\,\text{W}$?

Potential difference and power

A wire with length $L$ has resistance $R$. Its cross-section is a circle of radius $r$. Another wire, which also has a circular cross-section and is made from the same material, has resistance $\frac{1}{2}R$. What pair of radius and length might the second wire have?

Resistance and resistivity

A battery whose internal resistance is negligible can be joined between any two of the points $P$, $Q$, $R$ and $S$ in the resistor network shown. Which pairings will produce the greatest current and the least current in the battery?

Practical circuits

Kirchhoff’s second law is derived from a fundamental principle. Which principle is this?

Kirchhoff's laws

A potentiometer is used to investigate two cells. At the balance point, cell $X$ has a reading of $44\,\text{cm}$ and cell $Y$ has a reading of $70\,\text{cm}$. Which statement is not correct?

Practical circuits

A proton inside a nucleus undergoes $\beta^+$ decay. A neutron is one of the products. What are the remaining products?

Atoms, nuclei and radiation

Vectors $P$ and $Q$ have been drawn to scale. Which diagram shows the vector $(P + Q)$?

Scalars and vectors

One kind of hadron has no charge. It contains a down quark, a strange quark and one additional quark. What might the other quark be?

Fundamental particles

Using three different measuring instruments, $X$, $Y$ and $Z$, students measure the volume of a liquid. The actual volume of the liquid is $V$. Their measurements are shown. How many instruments are precise, and how many are accurate?

Errors and uncertainties

A sprinter takes part in a $100\,\text{m}$ race. Starting from rest, the sprinter accelerates uniformly at $2.5\,\text{m s}^{-2}$ until the speed reaches $10\,\text{m s}^{-1}$. After that, the speed stays constant right up to the finish. How long does the sprinter take to complete the race?

Equations of motion

A resultant force of $10\,\text{N}$ is applied to a body for $2.0\,\text{s}$. Which graph could represent how the momentum $p$ of the body varies with time $t$?

Momentum and Newton's laws of motion

The free-fall acceleration at the surface of planet $P$ is one tenth of the value at the surface of planet $Q$. At the surface of $P$, a body has mass $1.0\,\text{kg}$ and weight $1.0\,\text{N}$. What are the mass and the weight of that same body on the surface of planet $Q$?

Momentum and Newton's laws of motion

Two bodies moving in the same straight line undergo a perfectly elastic collision. Which statement has to be true?

Linear momentum and its conservation

Which statement would not be a reasonable estimate?

Errors and uncertainties

A ship with mass $8.4 \times 10^7\,\text{kg}$ is moving towards a harbour at speed $16.4\,\text{m s}^{-1}$. Using reverse thrust, it is able to keep a constant total stopping force of $920\,000\,\text{N}$. How long does it take to come to rest?

Momentum and Newton's laws of motion

A rigid, hollow sphere is placed far below the water surface and then set free from rest. An upthrust acts on it and drives it upwards towards the surface of the water. Which graph most accurately shows how its upward velocity $v$ varies with time $t$?

Non-uniform motion

A flat metal disc has radius $R$. Forces with magnitude $F$ act tangentially at the disc's edge. These forces lie in the plane of the disc. Which arrangement of forces produces only a torque of magnitude $2FR$?

Turning effects of forces

The diagram depicts the jib of a crane making an angle of $35^\circ$ with the vertical. A cable runs over a frictionless pulley and supports a load of $1830\,\text{N}$. The force $R$ exerted by the pulley on the cable acts along the line of the jib. The cable and the pulley are in equilibrium. What is the value of $R$?

Equilibrium of forces

What is one unit used for density?

Density and pressure

Which statement about energy is incorrect?

Energy conservation

An electric kettle has an input power rating of $1.50\,\text{kW}$ and an efficiency of $65.0\%$. It is turned on for $2.00\,\text{minutes}$. How much energy is transferred to the water in the kettle?

Potential difference and power

A gravitational force $F$ acts on a mass of $6.0\,\text{kg}$ on a planet. The mass is displaced by force $F$ by $30\,\text{m}$ in the same direction as the gravitational field. The work done by the field is $450\,\text{J}$. What are the force $F$ on the mass and the acceleration of free fall $g$ on the planet?

Gravitational potential energy and kinetic energy

A girl whose mass is $50\,\text{kg}$ runs up a staircase of $20$ steps in $7.0\,\text{s}$. Each step has a height of $25\,\text{cm}$. What is the useful average power output provided by the girl in climbing the staircase?

Gravitational potential energy and kinetic energy

In an experiment to determine the Young modulus of a metal, a wire made from the metal with diameter $0.25\,\text{mm}$ is held in place as shown. The wire runs from a clamp, over a frictionless pulley, and then to a second frictionless pulley, where loads $F$ are attached to it. A marker is fastened to the wire so that the initial total length of wire between the clamp and the marker is $3.70\,\text{m}$. A scale is fixed close to this marker. The graph shows how the reading on the scale changes with $F$. What is the Young modulus of the metal?

Stress and strain

Three of these quantities share the same unit. Which quantity is measured in a different unit?

SI units

A scientist is studying the properties of a new material. She draws a force-extension graph for the material up to its breaking point. Which statement has to be correct?

Elastic and plastic behaviour

A travelling sound wave in air has amplitude $x_0$ and intensity $I$. If the wave amplitude rises to $3x_0$, what is the wave’s new intensity?

Progressive waves

The way the displacement $y$ of a transverse wave on a rope varies with distance $x$ is shown at time $t = 0$. The wave has a frequency of $0.5\,\text{Hz}$. A point X on the rope is marked. The diagram shows the initial position of X together with four new positions. What is the position of X at time $t = 1\,\text{s}$?

Progressive waves

A microphone picks up a sound wave. Its output is linked to the Y-input of a cathode-ray oscilloscope (c.r.o.). The trace on the c.r.o. is shown. The time-base is set at $0.20\,\text{ms}$ per division. What is the frequency of the sound wave?

Progressive waves

A bat travels straight towards a stationary ultrasound detector at a speed of $25.0\,\text{m s}^{-1}$ while producing ultrasound pulses with frequency $40.0\,\text{kHz}$. The speed of sound in air is $330\,\text{m s}^{-1}$. What frequency is registered by the ultrasound detector?

Doppler effect for sound waves

An electromagnetic wave has a wavelength of $1.0 \times 10^{-7}\,\text{m}$. Which part of the electromagnetic spectrum does this wave fall into?

Electromagnetic spectrum

The diagram depicts a stationary wave on a string. Three nodes, $N_1$, $N_2$ and $N_3$, are shown on the stationary wave. Which statement is correct?

Stationary waves

In what situation does diffraction take place?

Diffraction

A student connects two loudspeakers to a signal generator. While the student moves from P to Q, he observes that the loudness of the sound repeatedly increases and decreases. What causes the loudness of the sound to vary?

Interference

A parallel beam of white light is directed normally at a diffraction grating. The second-order and third-order spectra overlap partly. Which wavelength in the third-order spectrum is seen at the same angle as the wavelength of $600\,\text{nm}$ in the second-order spectrum?

The diffraction grating

Which set of quantities consists solely of vectors?

Scalars and vectors

A pair of parallel metal plates is maintained at electric potentials of $+800\,\text{V}$ and $+1300\,\text{V}$. Which diagram shows the electric field between the metal plates most accurately?

Potential difference and power

The diagram illustrates two metal plates P and Q. A potential difference of $700\,\text{V}$ exists across the plates. Plate Q is earthed. What are the magnitude and the direction of the electric field at point R?

Potential difference and power

The current $I$ in a copper wire can be determined by using the equation shown. $I = Anvq$. What does the symbol $v$ stand for?

Electric current

The three resistors are connected in a circuit in the arrangement shown. The power dissipated in any resistor must not exceed $4.0\,\text{W}$. Determine the greatest voltage across XY.

Potential difference and power

Gold is occasionally chosen for use in tiny connecting wires inside electronic circuits. One gold wire has a length of $2.50 \times 10^{-3}\,\text{m}$ and a cross-sectional area of $6.25 \times 10^{-8}\,\text{m}^2$. The resistivity of gold is $2.30 \times 10^{-8}\,\Omega\,\text{m}$. Calculate the resistance of the wire.

Resistance and resistivity

A resistor X with resistance $40\,\Omega$ and a variable resistor are connected to a battery with electromotive force (e.m.f.) $12\,\text{V}$ and internal resistance $2.0\,\Omega$, as indicated. The resistance of the variable resistor is altered from $0$ to $40\,\Omega$. What is the change in power dissipated in resistor X?

Potential difference and power

Every resistor in resistor networks W, X, Y and Z has an equal resistance. Which list shows the networks arranged in order of increasing total resistance?

Resistance and resistivity

For the circuit diagram shown, the ammeter has a reading of zero. What is the resistance of resistor R?

Kirchhoff's laws

A neutron strikes a uranium-235 nucleus. One possible nuclear reaction formed is shown by the equation $^{235}_{92}\text{U} + {}^{1}_{0}\text{n} \rightarrow {}^{154}_{60}\text{Nd} + {}^{80}_{32}\text{Ge} + x$ in which $x$ stands for one or more particles. What particle(s) does $x$ stand for?

Atoms, nuclei and radiation

A nucleus Q is written as $^{y}_{x}\text{Q}$. Which one of the following is an isotope of Q?

Atoms, nuclei and radiation

The ammeter has been adjusted so that it reaches full-scale deflection when the current measured is $2.0\,\text{A}$. The diagram shows the reading on this ammeter while it is measuring a current. What current is the ammeter measuring?

Practical circuits

During $\beta^{-}$ decay, a neutron within a nucleus turns into a proton. Which statement gives the quark composition of the nucleus at the time of the decay?

Fundamental particles

The width of a table is recorded as $(50.3 \pm 0.1)\,\text{cm}$. Its length is recorded as $(1.40 \pm 0.01)\,\text{m}$. Determine the area of the table and its absolute uncertainty.

Errors and uncertainties

A stone is launched horizontally at time $t = 0$ and then falls. Air resistance can be ignored. The stone has a horizontal component of velocity $v_H$ and a vertical component of velocity $v_V$. Which graph shows how $v_H$ and $v_V$ change with time $t$?

Equations of motion

Two separate spheres have masses $2.0\,\text{kg}$ and $4.0\,\text{kg}$. They collide and afterwards move away from each other. While the collision takes place, the $2.0\,\text{kg}$ mass has an average acceleration of $8.0\,\text{m s}^{-2}$. What is the average acceleration of the $4.0\,\text{kg}$ mass?

Momentum and Newton's laws of motion

A mass is positioned on a frictionless slope that makes an angle of $30^\circ$ with the horizontal. It is then let go. What is its acceleration down the slope?

Momentum and Newton's laws of motion

At time $t = 0$, a parachutist starts from rest and drops straight down from a hot-air balloon. She descends for a certain distance before she opens her parachute. Which graph most accurately represents how the parachutist’s speed $v$ changes with time $t$?

Non-uniform motion