Acceleration

The photograph shows a rocket being launched at Cape Canaveral in the United States of America.

(Source: © Geopix / Alamy Stock Photo)

The table gives some information about the motion of the rocket during the first 5.0 seconds of its launch.

Calculate the final velocity of the rocket after 5.0 seconds.

Assume that the acceleration remains constant during this time.

Calculate the distance the rocket travels during the 5.0 seconds.

Assume that the acceleration remains constant during this time.

Sketch a velocity-time graph and a distance-time graph showing how the motion of the rocket changes during the first 5.0 seconds of its launch.

You do not need to include values on the axes.

An athlete jumps vertically from the ground.

The athlete has a mass of 85 kg, and leaves the ground with an upwards velocity of 4.5 m/s.

State the formula linking kinetic energy, mass and speed.

Calculate the athlete’s kinetic energy at a speed of 4.5 m/s.

At the maximum height of the jump, the athlete has a speed of 0 m/s.

State the increase in the amount of energy in the athlete’s gravitational potential energy store from the ground to the maximum height of the jump.

State the formula linking gravitational potential energy, mass, gravitational field strength and height.

Calculate the maximum height of the athlete’s jump.

Sketch a velocity‑time graph for the athlete’s jump from the ground to the maximum height of the jump. No numbers are required.

Assume there is no air resistance.

What feature of the velocity‑time graph gives the acceleration due to gravity?

Explain why the gravitational field strength on the Moon is different from the gravitational field strength on the Earth.

A student stretches a rubber band.

The photographs show a rubber band before and after it has been stretched.

State which energy store increases in the rubber band after it has been stretched.

State the main method of energy transfer when the rubber band is stretched.

State the source of the energy transferred to the rubber band.

The diagram shows a force-extension graph for a rubber band.

State how the graph shows that the rubber band does not obey Hooke’s law.

Explain how the graph shows that the rubber band is elastic.

The student stretches the rubber band and then releases it. The band moves vertically upwards.

The band travels with an initial speed of 13 m / s.

When the band reaches its maximum height above the student’s hand, the band has a speed of 0 m / s.

Calculate the maximum height that the band reaches.

Give your answer to 2 significant figures.

[acceleration due to gravity = −10 m / s²]

The band reaches its maximum height.

Explain the motion of the band as it falls from its maximum height to the ground.

Refer to forces in your answer.

You may assume

• the band does not rotate

• the band does not reach terminal velocity

A car accelerates with a constant driving force along a horizontal road and reaches its maximum speed.

This is the velocity-time graph for the car’s journey.

By drawing a tangent to the curve, determine the acceleration of the car at a time of 20 s.

acceleration =_........ ²

Determine the distance travelled by the car during the first 80 s of its journey.

Explain the motion of the car after 80 s.

The diagram shows a machine that can be used to measure the speed of fast‑moving protons.

At the start, the proton is attracted towards a negatively charged plate.

Give a reason why the proton is attracted to the negatively charged plate.

The proton accelerates at 1.90 × 10¹¹m / s² from rest to a speed of 1.38 × 10⁵m / s.

Show that the time taken for this acceleration is about 7 × 10^–7s.

The proton passes through a hole in the negatively charged plate and enters an area where there is a magnetic field.

The magnetic field exerts a force on the proton, as shown in the diagram.

This force causes the proton to follow a circular path without changing speed.

Give the direction of the magnetic field.

Suggest how increasing the strength of the magnetic field will affect the proton when it is moving in the magnetic field.

The graph shows how the velocity of a ball rolling down a long ramp changes with time.

Using the graph, calculate the acceleration of the ball.

acceleration =_........ ²

State the feature of the graph that gives the distance travelled by the ball.

Calculate the distance travelled by the ball in 2.5 seconds.

The table shows data for the ball after it has travelled for two different times.

A student suggests that these results obey the relationship:

Use data from the table to deduce whether the results support this suggestion.

A manometer is a device that can be used to measure the pressure difference between gas from a gas tap and the atmosphere.

When a gas tap is connected to the manometer, the liquid in the manometer moves due to the additional pressure of the gas.

Before connecting gas tap After connecting gas tap

The pressure difference is linked to the difference in height of the two surfaces of the liquid by the formula

pressure difference = density × g × height difference

The height difference between the two surfaces is 0.094 m.

Calculate the pressure difference between the gas from the gas tap and the atmosphere.

[for liquid, density = 14 000 kg / m³]

The graph shows how the velocity of the surface of the liquid changes with time from when the gas tap is opened to when the water level stops moving.

Use the graph to show that the distance travelled by the surface of the liquid is 4.7 cm.

Calculate the acceleration of the surface of the liquid.

acceleration =_........ cm / s²

Explain how the gas pressure changes if the temperature of the gas increases.

You should use ideas about particles in your answer.

The driver of a racing car makes a pit stop during a race to change the tyres on the racing car.

The area where the tyres are changed is called the pit lane.

Before entering the pit lane, the speed of the car must decrease for safety reasons.

The mass of the racing car is 830 kg.

The maximum braking force is 41 000 N.

Show that the maximum deceleration of the racing car is approximately 50 m / s².

The racing car is travelling at an initial speed of 72 m / s.

Calculate the minimum distance needed to decrease the speed of the racing car from 72 m / s to 26 m / s.

The racing car slows down using its brakes.

The brakes work using friction.

The brakes become very hot when the racing car slows down.

Using ideas about energy, explain why the brakes become hot.

The tyres of the racing car also get very hot during a race.

A mechanic has to handle the hot tyres during the pit stop.

They wear protective gloves which have several layers of insulating materials.

Explain how the layers of insulating materials in the gloves reduce the risk of the mechanic burning their hands on the hot tyres.

The diagram shows a balloon with a mass attached held at rest just below the surface of a deep pool of water.

The balloon and mass are released.

The graph shows the velocity-time graph for the balloon and mass as they fall through the water.

Use information from the graph to determine the terminal velocity of the balloon and mass.

Explain how the balloon reaches terminal velocity.

You should use ideas about forces acting on the balloon in your answer.

State the formula linking pressure difference, height, density and gravitational field strength.

Calculate the increase in pressure on the balloon when it has reached a depth of 25 m in the water.

[for water, density = 1000 kg/m³]

At the surface, the atmospheric pressure on the balloon is 1.010⁵Pa.

Show that the total pressure on the balloon at a depth of 25 m is 3.510⁵Pa.

At the surface, where the pressure is 1.010⁵Pa, the balloon has a volume of 0.46 m³.

Calculate the volume of the balloon at a depth of 25 m.

The graph shows how the thinking distance and the braking distance vary with the speed of a car.

Which of these does not affect thinking distance?

Which of these would increase the braking distance of the car?

Determine the stopping distance of the car when the speed of the car is 20 m / s.

State the formula linking average speed, distance moved and time taken.

Determine the reaction time of the driver of the car.

Calculate the mean braking acceleration of the car as it brakes to a stop from an initial speed of 30 m / s.

acceleration =_........ m / s²

The photograph shows a vertical drop ride at an amusement park.

The car is pulled to the top of a vertical shaft and then released from rest.

The car then falls freely because of the force of gravity.

Calculate the speed of the car when it has fallen 18 m.

State the formula linking kinetic energy, mass and speed.

The mass of the car and its passengers is 2.1 tonnes.

Calculate the kinetic energy of the car when it has fallen 18 m.

[1 tonne = 1000 kg]

The actual speed of the car when it has fallen 18 m is lower than the value calculated in (a).

Describe the energy transfers occurring from immediately before the car was released to when the car has fallen 18 m.

Refer to stores and transfers in your answer.

This question is about a parachutist.

A parachutist leaves a helicopter that is hovering above the ground.

The parachutist is initially at rest and falls vertically downwards.

Calculate the speed of the parachutist after they have fallen through a distance of 1300 m.

Ignore the effect of air resistance.

When the parachutist is much nearer to the ground, they open their parachute.

The parachutist slows down.

Explain the change in speed of the parachutist.

Use ideas about forces in your answer.

It is observed that from when the parachute opens to just before the parachutist touches the ground, the GPE store and the KE store of the parachutist both decrease, yet energy is still conserved.

Justify these observations.

A driver of a car sees an obstruction in the road ahead and must stop the car.

State the formula linking average speed, distance travelled and time taken.

A car travels at 21 m / s.

The driver’s reaction time is 0.14 seconds.

Calculate the distance travelled by the car during the driver’s reaction time.

The car experiences a braking force of 7600 N.

The car has a mass of 1200 kg.

State the formula linking force, mass and acceleration.

Calculate the acceleration of the car.

acceleration =_........ m / s²

Calculate the braking distance travelled as the speed of the car is reduced from 21 m / s to 0 m / s.

A person throws an object vertically upwards.

The speed-time graph shows how the speed of the object varies from the time it is thrown until reaching its maximum height.

Calculate the acceleration of the object.

acceleration =_........ m / s²

Calculate the distance the object travels to reach its maximum height.

A different object is dropped from rest and begins to fall.

The graph shows how the speed of this object varies with time.

Give the name of the two forces acting on the object as it falls.

Draw arrows on the diagram to show the forces acting on the object at B.

Explain the shape of the graph from A to C.

You should use ideas about forces to help your answer.

A student does an experiment to determine the acceleration due to gravity, g.

The diagram shows the apparatus used.

This is the student’s method.

• connect both light gates to a data logger

• drop a steel ball from rest at the top of the transparent tube

• record the speed of the ball at each light gate

• record the time taken for the ball to fall from light gate A to light gate B

The box shows the data recorded by the data logger.

Show that the acceleration of the steel ball is approximately 9.6 m/s².

acceleration =_........ ²

Explain why the student’s value for the acceleration of the steel ball is lower than the accepted value for the acceleration due to gravity, g.

Calculate the distance between the light gates.

The student changes the distance between the light gates by varying the position of light gate B.

The student measures the time taken for the steel ball to fall from light gate A to light gate B when the light gates are different distances apart.

The table shows the student’s results.

Plot a graph of the student’s results on the grid.

Draw the curve of best fit.

Explain how the graph shows that the steel ball is accelerating as it falls.

The motion of an object can be represented using graphs.

The graphs, P, Q, R and S, show different types of motion.

The table lists some types of motion.

Place one tick (✓) in each row of the table to show which graph represents which type of motion.

State the feature of a velocity‑time graph that can be used to determine the distance travelled by an object.

A speed camera is positioned at the side of a road.

The camera measures the speed of a vehicle on the road to determine whether the vehicle is travelling too fast.

The camera takes two photographs of the vehicle 0.25 s apart.

The photographs are used to measure the distance travelled by the vehicle during this time.

State the formula linking average speed, distance moved and time taken.

In the time between the two photographs, the car travels a distance of 6.5 m.

Calculate the average speed of the car.

The speed limit of the road is 80 kilometres per hour.

Determine whether the car is exceeding the speed limit.

The velocity-time graph shows how the velocity of a lorry changes with time.

Explain how the graph shows that the lorry has a constant acceleration.

State the formula linking acceleration, change in velocity and time taken.

Calculate the acceleration of the lorry.

acceleration =_........ ²

A student does an investigation to show how the velocity of a toy car changes when the car rolls down a ramp onto a table and hits a wooden block.

The graph shows how the velocity of the toy car changes with time.

Calculate the distance travelled by the car during the first 0.4 seconds.

Calculate the acceleration of the car between 0.40 s and 0.45 s.

acceleration =_........ ²

State the formula linking resultant force, mass and acceleration.

The car has a mass of 0.13 kg.

Calculate the resultant force on the car as it slows down.

A piece of soft material is fixed to the front of the toy car.

Explain how this will affect the gradient of the velocity-time graph after the car hits the block.

An aircraft travels along a runway.

The aircraft starts from rest and has a constant acceleration of 4.1 m/s².

Calculate the distance required to reach take‑off speed of 75 m/s.

The aircraft takes off and reaches its maximum height above the ground.

At maximum height, the background radiation count rate is higher than on the ground.

Explain what is meant by background radiation.

Suggest why there is a limit to the number of hours that an airline pilot can fly at maximum height.

The ink drop experiences a horizontal electrostatic force as it falls.

Explain the direction of the electrostatic force exerted on the ink drop by the charged plates.

On the diagram, draw the path of the ink drop as it falls between the charged plates until it hits the paper.

The ink drop experiences a horizontal force of 8.510^–7N when it is between the charged plates.

The mass of the ink drop is 1.110^–10kg.

Calculate the horizontal acceleration of the ink drop when it is between the charged plates.

acceleration =_........ ²

The ink drop has no initial horizontal velocity before it passes between the charged plates.

After passing between the charged plates, the horizontal velocity of the ink drop is 3.9 m/s.

Calculate the horizontal distance travelled by the ink drop as it passes between the charged plates.

Give your answer in mm.

Explain how another ink drop could be deflected in the opposite direction by a greater distance using the charged plates in the inkjet printer.

This question is about the movement of a train.

The diagram shows the train on a track.

The train starts braking at point P and stops moving at point Q.

The graph shows how the train’s velocity changes with time as the train travels from P to Q.

Calculate the acceleration of the train.

Calculate the distance travelled by the train from P to Q.

Draw a line on the graph to show how the train’s velocity will change if its initial velocity is the same but the braking force is lower.

This is a question about Io, a moon of Jupiter.

The diagram shows two jets of gas from volcanoes on Io.

One jet of gas is from the volcano Prometheus and the other is from the volcano Tvashtar.

Gas particles in the Prometheus jet leave the surface of Io and move vertically upwards.

The particles reach their maximum height when their speed is zero.

Some particles in the Prometheus jet reach a maximum height of 92 km.

Calculate the initial speed of these particles as they leave the surface of Io.

[acceleration due to gravity on Io 1.8 m/s²]

Before the gas particles leave the surface of Io, they are trapped in a chamber.

Explain how the gas particles exert a pressure on the walls of the chamber.

The Tvashtar chamber has the same volume as the Prometheus chamber and contains the same number of molecules of the same type of gas.

The temperature of the gas in the Prometheus chamber is 1200 K.

The temperature of the gas in the Tvashtar chamber is 1600 K.

The pressure of the gas in the Prometheus chamber is 8.2 kPa.

Calculate the pressure of the gas in the Tvashtar chamber.

Explain why the pressure inside the chambers increases when the temperature increases.

Use ideas about particles in your answer.

Explain why the particles from the Tvashtar chamber reach a greater maximum height than the particles from the Prometheus chamber.

The graph shows how the thinking distance and braking distance of a car vary with its initial speed.

80

A car has an initial speed of 35 m/s.

The brakes are applied and the car comes to a complete stop in the braking distance shown by the graph.

Calculate the mean braking acceleration of the car.

Evaluate how the thinking distance and the braking distance vary for different values of initial speed.

Refer to information from the graph in your answer.

A bus transports passengers.

The bus stops at certain points in its journey to let passengers get on or off the bus.

The distance-time graph shows part of the bus journey, with sections labelled A to G.

Give the letters of the sections where the bus is stationary.

Calculate the speed of the bus during section C of the journey.

Give your answer in m / s.

Explain what the graph shows about the speed of the bus in section E compared with the speed of the bus in section A.

Another bus travels a distance of 7.0 km in a time of 14 minutes.

This bus travels at a constant velocity.

Complete the velocity-time graph to show the motion of this bus.

A car is moving along a road.

The car has an initial velocity of 26 m / s.

The car then accelerates at 1. 2 m / s² until it reaches a velocity of 35 m / s.

State the formula linking acceleration, change in velocity and time taken.

Calculate the time taken for the car to accelerate to 35 m/s.

A radar speed gun is used to measure the speed of the moving car.

The radar speed gun emits radio waves towards the moving car.

The moving car reflects the radio waves back to a detector on the gun.

The detected radio waves have a different frequency from the emitted radio waves.

This change in frequency is used to measure the speed of the moving car.

Explain this change in frequency when the car is moving towards the radar speed gun.

The graph shows how the velocity of a parachute jumper changes with time.

At point A, the parachute jumper is falling at terminal velocity and has not yet opened her parachute.

Which statement is correct about the parachute jumper at point A?

Which is the best estimate of the distance fallen by the parachute jumper from the start until point A?

The parachute jumper opens her parachute at point B.

Her velocity decreases until she reaches terminal velocity again at point C.

Explain this change in velocity.

After point C, the parachute jumper continues to fall at a constant velocity.

As she falls, energy is transferred from a gravitational store.

Which store is the energy transferred into?

Diagram 1 shows a van accelerating along a horizontal road.

The horizontal forces acting on the van are shown.

Force X opposes the motion of the van.

State the name of force X.

The resultant force acting on the van is 1500 N.

Calculate the magnitude of force X.

[assume X is the only horizontal force opposing the motion of the van]

Diagram 2 shows the resultant force acting on the van when it brakes.

State the formula linking resultant force, mass and acceleration.

The mass of the van is 1900 kg.

Calculate the acceleration of the van when it brakes.

Give the unit.

The van was travelling at an initial speed of 18 m/s before braking and coming to rest.

Calculate the distance travelled by the van while it is braking.

[assume that the acceleration remains constant]

Describe two factors that would increase the braking distance.

When the van is fully loaded its mass increases to 2500 kg.

Calculate the time taken to bring the fully loaded van to rest when it is travelling at an initial speed of 18 m/s.

[assume that the resultant force during braking remains at 14 kN]