Motion (Cambridge (CIE) IGCSE Physics)

Model trains move along a track passing through two model stations. Students analyse the motion of a train. They start a digital timer as the train starts to move. They record the time that it enters Station A and the time it enters Station B.

Fig 1.1 below shows the time on entering Station A and the time on entering Station B.

Calculate the time taken from the train entering Station A to the train entering Station B. State your answer in seconds.

time taken = ....................................................... s 

A faster train takes 54 s to travel from Station A to Station B. The distance between the stations is 120 m.

Calculate the average speed of this train.

average speed = .................................................. m/s 

Fig. 1.2 shows the speed-time graph for a train travelling on a different part of the track.

Determine the total distance travelled by the train on this part of the track.

distance = ...................................................... m 

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Define acceleration.

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Fig. 1.1 shows the speed-time axes for the graph of the motion of a car.

(i) The car starts from rest.

  From time = 0 to time = 15 s, the car has a constant acceleration to a speed of 28 m/s.

  From time = 15 s to time = 32 s, the car has a constant speed of 28 m/s.

  From time = 32 s, the car has a constant deceleration of 2.0 m/s² until it comes to rest.

  On Fig. 1.1, draw the graph, using the space below for any calculations.

[5]

(ii) From time = 15 s to time = 32 s, the path of the car is part of a circle.

For this motion, state

1. the direction of the resultant force on the car,

2. what happens to the velocity of the car.

 [2]

Some cyclists are racing around a track. 

Fig.2.1 shows the speed-time graph for one cyclist.

(i) Tick the box that represents the cyclist travelling at constant speed.

A

B

C

D

[1]

(ii) Calculate the distance travelled by the cyclist in the first 5 seconds.

distance = ..................................................... m [3]

The length of the track is 250m. 

 Another cyclist goes around the track four times (four laps). This takes 80.0 seconds.

(i) Calculate the average speed of this cyclist.

average speed = ................................................. m/s [4]

(ii) A friend of the cyclist starts a stopwatch at the beginning of the race.

  Fig.2.2 shows the reading on the stopwatch when the cyclist has gone around the track once.

Fig.2.3 shows the reading on the stopwatch when the cyclist has gone around the track twice.

Calculate the time taken for the cyclist to go around the track during the second lap.

time = ....................................................... s [1]

Fig. 1.1 shows the speed–time graph of a person on a journey.

On the journey, he walks and then waits for a bus. He then travels by bus. He gets off the bus and waits for two minutes. He then walks again. His journey takes 74 minutes.

For the whole journey calculate:

(i) the distance travelled

distance = ......................................................... [3]

(ii) the average speed.

average speed = ......................................................... [2]

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State and explain which feature of a speed–time graph shows acceleration.

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State and explain the acceleration of the person at time = 40 minutes.

A person on roller skates makes a journey. Fig. 1.1 shows the speed-time graph for the journey.

The graph shows three types of motion.

Complete the table to show when each type of motion occurs. Use the letters shown on Fig. 1.1. Add a letter to each of the blank spaces. The first row is done for you.

Calculate the distance travelled between 60 s and 100 s. 

distance = ..................................................... m 

The size of the acceleration is greater than the deceleration.

Describe how Fig. 1.1 shows this.

Fig. 1.1 shows a water tank that is leaking. Drops of water fall from the tank at a constant rate.

A student uses a stopwatch to determine the time between two drops hitting the ground.

He sets the stopwatch to zero. He starts the stopwatch when the first drop hits the ground.

He stops the stopwatch after a further 30 drops have hit the ground.

The reading on the stopwatch is recorded and shown in Fig. 1.2.

(i) State the time taken for 30 drops to hit the ground.

 time = ...................................................... s [1]

(ii) Calculate the average time between two drops hitting the ground.

 time = ...................................................... s [2]

(iii) Explain why the student measures the time for 30 drops to hit the ground instead of measuring the time for one drop to hit the ground.

[1]

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Fig. 1.1 shows that the drops get further apart as they get close to the ground.

State why the drops get further apart.

In another experiment the student determines the speed of a falling weight at different times. The speed–time graph for his results is shown in Fig. 1.3.

Calculate the distance fallen by the weight in the first 1.5 s.

distance = ...................................................... m 

A lorry is travelling along a straight, horizontal road. Fig. 1.1 is the distance-time graph for the lorry.

Using Fig. 1.1, determine:

(i) the speed of the lorry at time t = 30 s

speed = ...........................................................[2]

(ii) the average speed of the lorry between time t = 60 s and time t = 120 s.

average speed = ...........................................................[2]

At time t = 30s, the total resistive force acting on the lorry is 1.4 × 10⁴ N.

(i) Using Fig. 1.1, determine the magnitude of the acceleration of the lorry at time t = 30 s.

acceleration = ...........................................................[1]

(ii) Determine the forward force on the lorry due to its engine at time t = 30 s.

forward force = ...........................................................[1]

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Describe the motion of the lorry between time t = 60 s and time t = 130 s.

A student reviews some data about athletes and footballers.

An athlete runs 12 km in 1.5 hours.

Calculate the athlete’s average speed in km/h.

average speed = ...................................................... km/h 

Fig. 2.1 shows the speed-time graph for a footballer for the first 15.0 seconds of a game.

(i) Use the graph in Fig. 2.1 to calculate the distance travelled by the footballer during the first 4.0 seconds.

distance = ...................................................... m [3]

(ii) Use the graph in Fig. 2.1 to determine when the footballer is moving with greatest acceleration.

Between .............................. s and .............................. s.

Give a reason for your answer.

[2]

Another footballer has a mass of 72kg.

Calculate the weight of this footballer.

weight = ...................................................... N 

A student drops a ball from a high window.

The mass of the ball is 0.12 kg.

Calculate the weight of the ball.

weight = .................................................... N

Fig. 3.1 shows the speed of the ball while it is falling. The points S, T, U, V and W are shown on the graph.

Draw one line from each section of the graph to the correct description of the motion.

One has been drawn for you.

Determine the distance fallen by the ball in section U – V of the graph.

distance = .................................................... m 

State the distance fallen by the ball in section V – W of the graph.

    distance = .................................................... m 

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A rocket is launched vertically upwards from the ground. The rocket travels with uniform acceleration from rest. After 8.0 s, the speed of the rocket is 120 m/s.

Calculate the acceleration of the rocket.

  acceleration = ........................................................ m/s² 

(i) On Fig. 1.1, draw the graph for the motion of the rocket in the first 8.0 s.

[1]

(ii) Use the graph to determine the height of the rocket at 8.0 s.    

height = .....................................................  [2]

(iii) From time = 8.0 s to time = 20.0 s, the rocket rises with increasing speed but with decreasing acceleration.

    From time = 20.0 s to time = 25.0 s, the rocket has a constant speed of less than 200 m / s.

   On Fig. 1.1, draw the graph for this motion. 

  [3]

Fig. 1.1 shows a speed-time graph for a student who is running.

Fig. 1.1

(i) Describe the movement of the student, as shown in Fig. 1.1.

[2]

(ii) Calculate the distance travelled by the student between 80s and 100s.

distance travelled = .......................................................m [3]

An athlete runs 630 m in 130 s on a flat section of a road and then 254 m in 40 s on a downhill slope.

Calculate the average speed for the total distance run by the athlete.

average speed = ...................................................m/s 

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A train of mass 5.6 × 10⁵ kg is at rest in a station.

At time t = 0 s, a resultant force acts on the train and it starts to accelerate forward.

Fig. 1.1 is the distance-time graph for the train for the first 120 s.

(i) Use Fig. 1.1 to determine:

1. the average speed of the train during the 120 s

average speed = ...........................................................[1]

2. the speed of the train at time t = 100 s.

 speed = ...........................................................[2]

(ii) Describe how the acceleration of the train at time t = 100 s differs from the acceleration at time t = 20 s.

[2]

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(i) The initial acceleration of the train is 0.75 m/s².

  Calculate the resultant force that acts on the train at this time.

resultant force = ...........................................................[2]

(ii) At time t = 120 s, the train begins to decelerate.

State what is meant by deceleration.

[1]

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A rocket is stationary on the launchpad. At time t = 0, the rocket engines are switched on, and exhaust gases are ejected from the nozzles of the engines. The rocket accelerates upward.

Fig. 1.1 shows how the acceleration of the rocket varies between time t = 0 and time t = t_f.

Define acceleration.

On Fig. 1.2, sketch a graph to show how the speed of the rocket varies between time t = 0 and time t = t_f.

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A rocket is now far from the Earth. The effect of the Earth’s gravity on the motion of the rocket is insignificant. As the rocket accelerates, its momentum increases.

(i) State the principle of the conservation of momentum.

[2]

(ii) Explain how the principle of the conservation of momentum applies to the accelerating rocket and the exhaust gases.

[2]

A student watches a car race around a track. He uses a stopwatch to measure the time for the car to make one lap of the track.

The student forgets to reset the stopwatch at the start of the race. Fig. 1.1 shows the time on the stopwatch at the start and the time after going around the track once.

Calculate the time the car takes to go around the track once, in seconds.  

time = ....................................................... s 

The length of the track is 4.0 km. The car goes around the track 20 times. The car takes 26 minutes and 40 seconds to complete the 20 laps.

Calculate the average speed of the car in m / s.

average speed = .................................................. m / s 

Fig. 1.2 shows a speed-time graph for the car during part of the race.

(i) State the section of the graph that shows the greatest acceleration.

...........................................................................................................................................

Explain your answer.

...........................................................................................................................................

[2]

(ii) Calculate the distance travelled by the car during the first 2.5 seconds.

distance = ...................................................... m [3]

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Fig. 1.1 shows the speed-time graph for a vehicle accelerating from rest.

Calculate the acceleration of the vehicle at time = 30s.

acceleration = ...........................................................

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Without further calculation, state how the acceleration at time = 100 s compares to the acceleration at time = 10 s. Suggest, in terms of force, a reason why any change has taken place.

Determine the distance travelled by the vehicle between time = 120 s and time = 160 s.

distance = ........................................................... 

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Define acceleration.

Fig. 1.1 shows two speed–time graphs, A and B, and two distance–time graphs, C and D.

Describe the motion shown by:

(i) graph A

[2]

(ii) graph B

[2]

(iii) graph C

[1]

(iv) graph D

[1]

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Fig. 1.1 shows the axes of a distance-time graph for an object moving in a straight line.

(i) On Fig. 1.1, draw between time = 0 and time = 10 s, the graph for an object moving with a constant speed of 5.0 m/s. Start your graph at distance = 0 m.

State the property of the graph that represents speed.

[2]

(ii) Between time = 10 s and time = 20 s the object accelerates. The speed at time = 20 s is 9.0 m/s.

Calculate the average acceleration between time = 10 s and time = 20 s.

acceleration = ...........................................................[2]

Fig. 1.2 shows the axes of a speed-time graph for a different object.

(i) The object has an initial speed of 50 m/s and decelerates uniformly at 0.35 m/s² for 100 s.

On Fig. 1.2, draw the graph to represent the motion of the object.

[2]

(ii) Calculate the distance travelled by the object from time = 0 to time = 100 s.

distance = ...........................................................[3]

Fig. 2.1 shows students getting onto a school bus.

A student describes part of the journey.

The bus accelerates from rest at a constant rate for 10 s. It reaches a maximum speed of 10 m/s.

The bus maintains a constant speed of 10 m/s for 60 s.

The bus then decelerates at a constant rate for 15 s, until it stops.

On Fig. 2.2, draw the speed-time graph for this part of the journey made by the bus.

On another part of the journey, the average speed of the bus is 7.5 m/s.

Calculate the distance the bus travels in 150 s.

distance = ..................................................... m