Equations of motion

An object starts with velocity $u$ and moves with acceleration $a$. It travels along a straight path, covers a displacement $s$ and ends with final velocity $v$. These quantities are linked by the equation shown below. $v^2 = u^2 + 2as$ What condition has to be met for this equation to be valid for the object's motion?

Feb/March 2016

A car is moving at constant velocity. The brakes are then applied, so it undergoes uniform deceleration. Which graph shows how the velocity $v$ of the car varies with distance $s$?

Feb/March 2016

A ball is projected over level ground. Which statement best describes how the ball moves if air resistance is neglected?

Feb/March 2016

Define acceleration in physics.

Feb/March 2016

An aircraft, starting from rest on a runway, reaches a speed of $85\,\text{km h}^{-1}$ over a distance that does not exceed $1.20\,\text{km}$. What minimum constant acceleration is required for the aircraft?

Feb/March 2017

A radio-controlled toy car moves in a straight line for $15\,\text{s}$. The graph shows how the velocity $v$ of the car changes with time $t$. What is the average velocity of the toy car for the journey represented by the graph?

Feb/March 2017

An electron moves in a straight line through a vacuum at a constant speed of $1.5 \times 10^{7}\,\text{m s}^{-1}$. It enters a uniform electric field at point A, as shown in Fig. 5.1. It keeps travelling in the same direction until the electric field brings it to rest at point B. The distance AB is $2.0\,\text{cm}$.

Feb/March 2017

A velocity-time graph for an object is shown. How may the object's total displacement be found?

Feb/March 2018

A girl throws a ball straight upwards. The ball takes $3.20\,$s to come back to her hand. Assume air resistance can be ignored. What is the initial speed at which the ball is thrown?

Feb/March 2018

Complete Fig. 1.1 by showing whether acceleration, speed, and power are vectors or scalars.

Feb/March 2018

A stone is projected vertically upwards from a point $12\,\text{m}$ above the sea. After $3.4\,\text{s}$, it falls into the sea below. Air resistance is negligible. At what speed was the stone released when it was thrown?

Feb/March 2019

A car travels along a straight road with uniform acceleration. Oil drips from the car at a rate of one drop every two seconds. The diagram illustrates the separations between three consecutive oil drops on the road. The distances shown are $9.0\,\text{m}$ and $12.0\,\text{m}$. Determine the acceleration of the car.

Feb/March 2020

A massive particle travels in a horizontal straight path through a uniform electric field in a vacuum, with the electric field acting vertically. The motion of the particle is affected significantly by gravity. What might be the direction of the electric field, and what sign, if any, does the charge on the particle have?

Feb/March 2021

Four cars, A, B, C and D, begin from rest and travel along a straight line. Each car takes the same time to increase its velocity to $60\,\text{km h}^{-1}$. Their velocity-time graphs are given. Which car reaches a velocity of $60\,\text{km h}^{-1}$ over the shortest distance?

Feb/March 2021

A cannon launches a cannonball with initial speed $v$ at an angle $\alpha$ above the horizontal. Which equation gives the maximum height $H$ attained?

Feb/March 2021

How may the acceleration of an object be found?

Feb/March 2022

A sprinter records a time of $11.0\ \text{s}$ for a $100\ \text{m}$ race. At the start, she accelerates uniformly from rest until she reaches a speed of $10\ \text{m s}^{-1}$. After that, she continues at a constant speed of $10\ \text{m s}^{-1}$ up to the finish line. What is the sprinter’s uniform acceleration during the first part of the race?

Feb/March 2022

At point $P$, water leaves the end of a hose pipe with a horizontal velocity of $6.6\,\text{m s}^{-1}$, as shown in Fig. 2.1. The point $P$ is at height $h$ above the ground, and the water lands at point $Q$. The horizontal separation between $P$ and $Q$ is $3.5\,$m. Air resistance is negligible. Between $P$ and $Q$, treat the water as a collection of non-interacting droplets, with only each droplet’s weight acting on it.

Feb/March 2022

A ball is let go from rest at position $X$ at time zero. At $1.0\text{ s}$, it undergoes an inelastic bounce off a horizontal surface and then rises, arriving at the highest point of its first rebound at $1.5\text{ s}$. What is the ball's total displacement from its starting position $X$ at $1.5\text{ s}$?

Feb/March 2024

What does acceleration mean?

Feb/March 2024

A basketball player throws a ball straight downwards at a speed of $2.4\,\text{m s}^{-1}$ from a height of $0.90\,\text{m}$. The effect of air resistance can be ignored. What speed does the ball have when it reaches the ground?

Feb/March 2024

Define the term acceleration.

Feb/March 2024

An aircraft begins from rest on a runway and reaches a take-off speed of $85\,\text{km h}^{-1}$ over a distance of at most $1.20\,\text{km}$. What minimum constant acceleration is required for the aircraft?

Feb/March 2025

A projectile is launched upward from level ground. It starts with an initial velocity of $20\,\text{m s}^{-1}$ at an angle of $45^{\circ}$ to the horizontal. Air resistance is negligible. Which statement gives the speed of the object from the moment it is fired until just before it lands on the ground again?

Feb/March 2025

The diagram presents a velocity-time graph for a vehicle. Travelling at $4.0\,\text{m s}^{-1}$, the vehicle starts to accelerate when time $= 0$. What is the vehicle’s acceleration at time $= 3.0\,\text{s}$?

May/June 2010

A small steel ball is released from rest and falls freely under gravity. Which graph best shows how the height $h$ of the ball changes with time $t$?

May/June 2010

A small steel ball is dropped from rest and moves freely under gravity. Which graph best shows how the height $h$ of the ball varies with time $t$?

May/June 2010

The diagram presents a velocity-time graph for a vehicle. At time $= 0$, the vehicle is travelling at $4.0\,\text{m s}^{-1}$ and then starts to accelerate. What is the vehicle’s acceleration at time $= 3.0\,\text{s}$?

May/June 2010

A small steel ball is dropped from rest and moves freely under gravity. Which graph best shows how the height $h$ of the ball changes with time $t$?

May/June 2010

The diagram presents a velocity-time graph for a vehicle. At time $= 0$, the vehicle, travelling at $4.0\,\text{m s}^{-1}$, starts to accelerate. What is the vehicle’s acceleration at time $= 3.0\,\text{s}$?

May/June 2010

An object's distance $s$ after time $t$ can be written as $s = \frac{1}{2}at^2$, where $a$ is its acceleration. State two conditions that must be true for this formula to describe the object's motion.

May/June 2010

The diagram shows a charged particle moving towards a pair of charged parallel plates in a vacuum. Which row gives the horizontal and vertical components of its motion while it passes between the plates?

May/June 2011

The graph illustrates how the acceleration of an object travelling in a straight line changes with time. Which graph shows how the velocity of the object varies with time?

May/June 2011

At time zero, a ball is released from rest. After $1.0\,\text{s}$, it makes an inelastic bounce off a horizontal surface and then rises again, reaching the highest point of its first rebound after $1.5\,\text{s}$. What is the ball’s total displacement from its starting position after $1.5\,\text{s}$?

May/June 2011

A bullet is launched horizontally at speed $v$ from a rifle. During a brief time $t$ after it leaves the rifle, gravity is the only force acting on its motion. The acceleration of free fall is $g$. Which expression gives the horizontal distance travelled in time $t$ divided by the vertical distance travelled in time $t$?

May/June 2011

A tennis ball is dropped and falls freely through air from the top of a tall building. Which graph most accurately shows how the distance $s$ fallen changes with time $t$?

May/June 2011

A small glider travels along a smooth horizontal air track, as shown below. There is a perfectly elastic buffer at each end of the air track. Which graph shows how the velocity v of the glider changes with time t as it moves between the two buffers?

May/June 2011

The diagram illustrates a charged particle as it moves towards a pair of charged parallel plates in a vacuum. Which row gives the horizontal and vertical components of its motion as it passes between the plates?

May/June 2011

The graph indicates how an object’s acceleration, while travelling along a straight line, changes with time. Which graph shows how the object’s velocity changes with time?

May/June 2011

A ball is let go from rest at time zero. After $1.0\,\text{ s}$ it strikes a horizontal surface inelastically and rebounds, reaching the highest point of its first bounce after $1.5\,\text{ s}$. What is the ball's total displacement from its starting position after $1.5\,\text{ s}$?

May/June 2011

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

May/June 2012

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?

May/June 2012

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

May/June 2012

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?

May/June 2012

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 $t = T$?

May/June 2012

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?

May/June 2012

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?

May/June 2012

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

May/June 2012

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

May/June 2012

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 $0.50T$?

May/June 2012

A ball is projected straight downwards towards the ground and bounces back, as shown in Fig. 2.1. When the ball passes A, its speed is $8.4\,\text{m s}^{-1}$. Point A is $5.0\,\text{m}$ above the ground. The ball strikes the ground and rebounds to B. Assume air resistance is negligible.

May/June 2012

A cannon launches a cannonball with initial speed $v$ at an angle $\alpha$ above the horizontal. Which equation gives the maximum height $H$ attained?

May/June 2013

An electron beam enters an electric field and is turned away by it. Diagram 1 shows an electric field lying in the plane of the paper. Diagram 2 shows an electric field acting at right angles 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 electrons’ path within the field?

May/June 2013

A goods train travels through a station at a constant speed of $10\,\text{m s}^{-1}$. An express train is stationary at the station. At the instant the goods train passes, the express train starts from the station with a uniform acceleration of $0.5\,\text{m s}^{-2}$. The two trains travel in the same direction along straight, parallel tracks. After how much time does the express train overtake the goods train?

May/June 2013

A ball is projected vertically upward. If air resistance is ignored, which statement is correct?

May/June 2013

A positively charged particle is launched into a uniform electric field. Which diagram shows the route followed by the particle in the electric field?

May/June 2013

The diagram illustrates a system designed to prevent trains from going above a safe speed. Trains approaching from the left move with a speed of $50\,\text{m s}^{-1}$. At marker 1, the driver has to use the brakes so that the train slows down at a constant rate and reaches marker 2 with a speed of no greater than $10\,\text{m s}^{-1}$. The train has a detector which records the times at which it passes each marker and activates an emergency brake if the interval between passing marker 1 and marker 2 is under $20\,\text{s}$. At what distance from marker 2 should marker 1 be positioned?

May/June 2013

A ball is let go from rest above a horizontal surface and rebounds several times. The graph indicates how a quantity $y$ changes with time for this ball. What is the quantity $y$?

May/June 2013

The diagram illustrates the trajectory of a charged particle in a uniform electric field, with vertical field lines. What might produce a path of this form?

May/June 2013

A double-ended launching device sends two identical steel balls $X$ and $Y$ out at precisely the same time. The diagram indicates the balls’ initial velocities. Both are projected horizontally, although $Y$ has the larger speed. Which statement best explains what an observer would see?

May/June 2013

At time $t = 0$, a body starts from rest and travels in a straight line with constant acceleration. When the time is $t$, the body is at a distance $s$ from its rest position. A graph of $s$ against $t^{2}$ is plotted, as shown. Which statement gives the acceleration of the body?

May/June 2013

A student travels from A to B along the route shown in Fig. 2.1. The student takes time $t$ to travel from A to B.

May/June 2013

An object is projected vertically upwards on the Moon with a velocity of $5.2\,\text{m s}^{-1}$. The Moon’s acceleration due to gravity is $1.62\,\text{m s}^{-2}$. What time does the object take to return to the point from which it was launched?

May/June 2014

The graph illustrates the way in which the acceleration of an object moving along a straight line changes with time. At the start, the object is at rest. Which graph shows how the velocity of the object changes with time over the same time interval?

May/June 2014

A shot-put champion speeds up a $7.0\,\text{kg}$ metal ball along a straight path. Starting from rest, the ball reaches a speed of $12\,\text{m s}^{-1}$ over a distance of $1.2\,\text{m}$. What is the average resultant force acting on the metal ball?

May/June 2014

An electron moves into a region of space containing a uniform electric field $E$, as illustrated. At the start, the electron travels parallel to the electric field and in the same direction as it. What path does the electron then follow, and how does its speed change?

May/June 2014

An experiment is carried out to determine the acceleration of free fall $g$. A body drops between two fixed points. The four readings shown below are recorded. Which reading is not needed for the calculation of $g$?

May/June 2014

In a cathode-ray tube, an electron moves with uniform acceleration in a straight line, increasing its speed from $4 \times 10^{3}\,\text{m s}^{-1}$ to $2 \times 10^{7}\,\text{m s}^{-1}$ across a distance of $10\,\text{mm}$. What is the electron's acceleration?

May/June 2014

Define the term velocity.

May/June 2014

An insect launches upwards with an initial vertical velocity of $1.0\,\text{m s}^{-1}$ and attains a greatest height of $3.5 \times 10^{-2}\,\text{m}$. If the deceleration is constant, what is the magnitude of the deceleration?

May/June 2015

A body moving with uniform acceleration $a$ changes its velocity from $u$ to $v$ over a time $t$. Which expression would not produce the correct displacement of the body during the time $t$?

May/June 2015

A stone is launched horizontally from the summit of a cliff. Air resistance may be ignored. Which graph illustrates how the vertical component of the stone’s velocity changes with time?

May/June 2015

A sprinter completes a $100\,\text{m}$ race in a straight line. Starting from the blocks, he increases his speed with a constant acceleration of $2.5\,\text{m s}^{-2}$ until he reaches a top speed of $10\,\text{m s}^{-1}$. He then continues at this speed until the finish line is crossed. How long does the sprinter take to complete the race?

May/June 2015

The electric car’s velocity varies as illustrated. What is the car’s acceleration?

May/June 2015

Define speed and velocity, then use those definitions to explain why one of these quantities is scalar while the other is vector.

May/June 2015

A stone is projected straight upwards. Fig. 2.1 shows how the displacement $s$ of the stone varies with time $t$.

May/June 2015

A charged particle is travelling through a uniform electric field. During the particle’s motion caused by the field, which quantity remains at a constant non-zero value?

May/June 2016

A car speeds up with uniform acceleration from velocity $u$ to velocity $v$ over a time interval of $t$. On the graph, which area is equal to the distance the car travels in time $t$?

May/June 2016

A student uses a spring gun to fire a steel ball with a constant horizontal velocity. He changes the height $h$ of the gun and records the horizontal displacement $r$ of the ball as it lands on the ground. Which graph shows how the horizontal displacement $r$ varies with height $h$?

May/June 2016

At time $t = 0$, cars X and Y are located as illustrated. Both are moving in the same direction. X is $50\,\text{m}$ behind Y and moves with a constant velocity of $30\,\text{m s}^{-1}$. Y moves with a constant velocity of $20\,\text{m s}^{-1}$. What is the value of $t$ when X is level with Y?

May/June 2016

The acceleration of free fall on the Moon is $1.6\ \text{m s}^{-2}$. There is no atmosphere on the Moon. An astronaut on the Moon’s surface lets go of a feather. Which graph shows how the feather’s speed changes with time during the first second of its fall?

May/June 2016

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

May/June 2016

A ball moves in a straight line up a ramp and then returns down the ramp along the same route. Which graph shows how the ball’s velocity changes with time?

May/June 2016

A ball is projected with velocity $V$ at an angle $\theta$ above the horizontal. The acceleration due to free fall is $g$. Take air resistance to be negligible. What are the horizontal displacement $x$ and the vertical displacement $y$ after time $t$?

May/June 2016

A ball is projected from point $P$ with an initial velocity $u$ of $12\,\text{m s}^{-1}$ at $50^\circ$ above the horizontal, as shown in Fig. 2.1. The ball attains its greatest height at $Q$. Air resistance is negligible.

May/June 2016

Define the term acceleration.

May/June 2016

A ball is dropped from rest above a rigid, horizontal surface. The graph shows how the velocity of the bouncing ball changes with time. At what point on the graph does the ball attain its greatest height after the first bounce?

May/June 2017

A ball is projected upward at an angle of $45^{\circ}$ above the horizontal ground. After a brief flight, the ball lands back on the ground. Assume that air resistance can be neglected. What quantity is never zero during the ball’s flight?

May/June 2017

A constant force acts on a block, driving it across a horizontal surface with no friction. Starting from rest, the block travels a fixed distance. What is the connection between the block’s final speed $v$ and its mass $m$?

May/June 2017

On a planet, a projectile launched vertically upward takes $12.5\,\text{ s}$ to come back to where it started. Its greatest height is $170\,\text{ m}$. There is no atmosphere on the planet. Determine the acceleration of free fall on this planet?

May/June 2017

A displacement-time graph for a toy car is displayed. Which graph shows how the car’s velocity $v$ changes with time?

May/June 2017

The graph illustrates how a quantity $y$ changes with a quantity $x$ for an object falling through air at constant (terminal) velocity in a uniform gravitational field. Which quantities might $x$ and $y$ be?

May/June 2017

Define the term velocity.

May/June 2017

A tennis ball is dropped and falls through the air from the top of a tall building. Which graph best shows how the distance $s$ fallen changes with time $t$?

May/June 2018

The velocity of an object varies with time $t$ as illustrated. Which graph most accurately represents how the displacement $s$ of the object changes with time $t$?

May/June 2018

At time $t = 0$, a projectile is projected at an angle to the horizontal. It moves above horizontal ground, as illustrated. Take air resistance to be negligible. Which graph most accurately shows how the speed of the projectile changes with $t$ from launch until it reaches the ground?

May/June 2018

A particle of mass $m$ and charge $+q$ is projected into a uniform electric field with speed $v$. At the start, its velocity is at right angles to the electric field. As it passes through the field, it is displaced by distance $d$, as shown. A second particle with mass $2m$, charge $+q$ and speed $v$ enters the electric field along the same route. What distance is this particle deflected by in the electric field?

May/June 2018

A rock on the surface of Mars is thrown straight upwards with an initial speed of $9.4\,\text{m s}^{-1}$. It reaches a maximum height of $12\,\text{m}$ above the surface. Assume that Mars has no atmosphere. What is the acceleration of free fall near the surface of Mars?

May/June 2018

A $\beta^{-}$ particle emitted by a radioactive source is moving through a vacuum with kinetic energy $460\,\text{eV}$. It enters a uniform electric field at right angles and then follows the route shown in Fig. 7.1.

May/June 2018

A ball is projected vertically upwards towards a ceiling and then bounces back, as shown in Fig. 3.1. It is launched with speed $9.6\,\text{m s}^{-1}$ and needs $0.37\,\text{s}$ to get to the ceiling. It remains in contact with the ceiling for a further $0.085\,\text{s}$ before departing with speed $3.8\,\text{m s}^{-1}$. The ball has mass $0.056\,\text{kg}$. Air resistance may be ignored.

May/June 2018