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GCSE · Physics

P5a Motion: Speed, Velocity and Acceleration

AQA 8464 · Calculator allowed · about 85 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Investigating the acceleration of a trolley

Original text written for Revision Library.

A student wants to determine the acceleration of a trolley as it runs down a ramp. She sets up a ramp with two light gates fixed at different points along its length, both connected to a data logger. An interrupt card of known length is attached to the top of the trolley. As the trolley runs down the ramp, the interrupt card passes through each light gate in turn; the data logger records how long the card takes to cross each gate, and it also records the time taken for the trolley to travel between the two gates. Questions 14 to 16 and Question 20 refer to this investigation.

Motion graphs and their gradients carry specific physical meanings.

(a)State what is represented by the gradient of a distance-time graph.(1)

(b)State what is represented by the gradient of a velocity-time graph.(1)

(c)State what is represented by the area under a velocity-time graph.(1)

(d)State the SI unit of acceleration.(1)

(Total for Question 1 is 4 marks)

Distance and displacement both describe how far an object has moved, but they are not always equal in value.

(a)State what is meant by distance travelled.(1)

(b)State what is meant by displacement.(1)

(c)Priya cycles 800 m due north from her house to a park, travelling in a straight line. She then cycles back home along the same straight route. Calculate (i) the total distance she travels, and (ii) her overall displacement for the whole journey.(2)

(Total for Question 2 is 4 marks)

State one difference between speed and velocity.

(Total for Question 3 is 2 marks)

Chloe runs 300 m along a straight track in a time of 250 s. Use average speed = distance / time to calculate her average speed.

(Total for Question 4 is 2 marks)

The average speed of a car driving through a UK town centre is about 13 m/s.

(a)Convert this speed to km/h, using 1 m/s = 3.6 km/h.(1)

(b)A driver claims this speed is 'about 30 miles per hour'. Given that 1 km/h is approximately 0.62 mph, calculate this speed in mph and comment on whether the driver's claim is reasonable.(2)

(Total for Question 5 is 3 marks)

The list below gives typical average speeds for different forms of transport: walking pace = 1.5 m/s; cycling = 5.5 m/s; a car in a built-up area = 13 m/s; a car on a UK motorway = 31 m/s; a train = 55 m/s.

(a)A train travels at its typical speed, given above, for a distance of 11 km. Calculate how long this journey takes, in seconds.(2)

(b)Amara, a cyclist, rides 220 m in a time of 40 s. Calculate her average speed, and state whether this matches the typical cycling speed given above.(3)

(Total for Question 6 is 5 marks)

The graph shows the distance travelled by a cyclist, Kwame, during a 100 second journey along a straight, flat road.

(a)Describe Kwame's motion between t = 40 s and t = 70 s.(1)

(b)Calculate Kwame's speed during the first 40 seconds of the journey.(2)

(c)Calculate Kwame's speed between t = 70 s and t = 100 s, and state what the shape of the graph in this section tells you about the direction he is travelling in.(2)

(Total for Question 7 is 5 marks)

The velocity-time graph shows the motion of a bus over a 51 second period, as it pulls away from a stop. Describe the bus's motion in each of the three stages shown on the graph, referring to the gradient in each stage.

(Total for Question 8 is 3 marks)

Using the velocity-time graph in Question 8, calculate the bus's acceleration during the first 15 seconds, as it speeds up from the stop.

(Total for Question 9 is 3 marks)

A go-kart driven by Leon starts from rest. The table shows its velocity at different times after starting.
Time (s): 0, 2, 4, 6
Velocity (m/s): 0, 3, 6, 9
Calculate the go-kart's acceleration during two different time intervals, and use your results to explain why its acceleration is constant.

(Total for Question 10 is 4 marks)

Using the velocity-time graph in Question 8, calculate the total distance the bus travels during the whole 51 second journey. (Hint: the distance travelled is equal to the area under the velocity-time graph.)

(Total for Question 11 is 5 marks)

Zara, a skater, accelerates from 2.0 m/s to 8.0 m/s in a time of 4.0 s. Use acceleration = change in velocity / time taken (a = (v - u) / t) to calculate her acceleration.

(Total for Question 12 is 3 marks)

Nia, a cyclist, decelerates from 6.0 m/s to rest at a constant rate of 1.2 m/s^2. Use a = (v - u) / t to calculate how long it takes her to stop.

(Total for Question 13 is 4 marks)

Describe how the equipment described above could be used to determine the trolley's acceleration as it moves down the ramp.

(Total for Question 14 is 4 marks)

In the investigation, the trolley's interrupt card has a length of 5.0 cm (0.050 m). The data logger records: time to cross light gate 1 = 0.125 s; time to cross light gate 2 = 0.050 s; time taken to travel between the two light gates = 0.80 s.

(a)Calculate the trolley's velocity as it passes through light gate 1. Use velocity = length of card / time to cross the gate.(2)

(b)Calculate the trolley's velocity as it passes through light gate 2.(2)

(c)Calculate the trolley's acceleration between the two light gates. Use acceleration = change in velocity / time taken.(2)

(Total for Question 15 is 6 marks)

The student repeats the investigation three times for the same ramp angle and calculates a mean acceleration.

(a)State one reason why repeating the experiment and calculating a mean improves the reliability of the acceleration value.(1)

(b)Suggest one improvement to the method, other than repeating it, that would increase the accuracy of the velocity measurements, and explain how it would help.(2)

(Total for Question 16 is 3 marks)

Higher tier only. Ibrahim, a skateboarder, has an initial velocity of 2.0 m/s and accelerates at a constant 1.5 m/s² over a distance of 6.0 m. The equation sheet gives v² = u² + 2 a s. Calculate his final velocity, v.

(Total for Question 17 is 4 marks)

Higher tier only. Freya rides an electric scooter at 24 m/s. She decelerates uniformly at 3.0 m/s² until she comes to rest. Use v² = u² + 2 a s (with the deceleration taken as negative) to calculate the distance she travels while decelerating.

(Total for Question 18 is 4 marks)

Higher tier only. Callum's remote-control car accelerates uniformly from rest. After accelerating for 8.0 s, it reaches a velocity of 12 m/s.

(a)Calculate the car's acceleration during this time, using a = (v - u) / t.(2)

(b)Calculate the distance travelled during the 8.0 s of acceleration, using v² = u² + 2as.(2)

(c)Check your answer to part (b) by instead calculating the distance using the area under a velocity-time graph for this section of the journey. State whether the two methods agree.(2)

(Total for Question 19 is 6 marks)

Aaliyah investigates how the acceleration of a trolley down the ramp depends on the height of one end of the ramp. She raises the ramp to different heights and, for each height, uses two light gates and an interrupt card (as described above) to calculate the trolley's acceleration. She plots a graph of acceleration against ramp height, and repeats each height three times. Evaluate this method, discussing how Aaliyah could improve the validity, accuracy and reproducibility of her results, and how she could use her graph to reach a valid conclusion.

(Total for Question 20 is 6 marks)

Mark scheme · P5a Motion: Speed, Velocity and Acceleration

Question 1

(a) B1 speed (oe average speed)
(a) Answer: Speed
(b) B1 acceleration
(b) Answer: Acceleration
(c) B1 distance travelled (oe displacement)
(c) Answer: Distance travelled
(d) B1 m/s² (oe metres per second squared)
(d) Answer: m/s²

Question 2

(a) B1 the total length of the path travelled by an object, regardless of direction, oe
(a) Answer: The total length of the path travelled, regardless of direction.
(b) B1 the straight-line distance from an object's starting point to its finishing point, in a stated direction (a vector), oe
(b) Answer: The straight-line distance from the start point to the finish point, in a stated direction.
(c) B1 distance = 1600 m (oe 800 + 800)
(c) B1 displacement = 0 m (oe zero, since she returns to her starting point)
(c) Answer: Distance = 1600 m; displacement = 0 m

Question 3

B1 speed has a magnitude only (it is a scalar quantity)
B1 velocity has a magnitude and a stated direction (it is a vector quantity)
Answer: Speed has magnitude only (a scalar); velocity has both magnitude and a stated direction (a vector).

Question 4

M1 substitutes: speed = 300 / 250
A1 1.2 m/s cao
Answer: 1.2 m/s

Question 5

(a) B1 46.8 km/h (accept 47 km/h to 2 s.f.)
(a) Answer: 46.8 km/h (47 km/h to 2 s.f.)
(b) M1 ft substitutes: 46.8 x 0.62 (allow use of their part (a) answer)
(b) B1 awrt 29 mph, with a valid comment, e.g. 'this is close to the claimed 30 mph (within about 1 mph), so the claim is reasonable', oe
(b) Answer: Approximately 29 mph; this is close to the driver's claim of 30 mph, so the claim is reasonable.

Question 6

(a) M1 converts 11 km to 11000 m and substitutes: time = 11000 / 55
(a) A1 200 s cao
(a) Answer: 200 s
(b) M1 substitutes: speed = 220 / 40
(b) A1 5.5 m/s cao
(b) B1 yes, this exactly matches the typical cycling speed of 5.5 m/s given above, oe
(b) Answer: 5.5 m/s; this matches the typical cycling speed given above.

Question 7

(a) B1 he is stationary/at rest (not moving); his distance from the start stays constant at 200 m, oe
(a) Answer: He is stationary; his distance from the start stays at 200 m.
(b) M1 substitutes: speed = 200 / 40
(b) A1 5.0 m/s cao
(b) Answer: 5.0 m/s
(c) B1 awrt 6.7 m/s (200 / 30)
(c) B1 he is travelling back towards his starting point; the negative gradient shows his distance from the start is decreasing, oe
(c) Answer: 6.7 m/s; he is travelling back towards his starting point.

Question 8

B1 stage 1 (0-15 s): straight line with a constant positive gradient, sloping up from the origin; the bus is accelerating (speeding up) at a constant rate
B1 stage 2 (15-45 s): horizontal line (zero gradient); the bus travels at a constant velocity of 12 m/s
B1 stage 3 (45-51 s): straight line with a constant negative gradient, sloping down to zero; the bus is decelerating (slowing down) at a constant rate, coming to rest
Answer: Stage 1: constant acceleration (speeding up). Stage 2: constant velocity (zero gradient). Stage 3: constant deceleration, coming to rest.

Question 9

M1 identifies change in velocity = 12 - 0 = 12 (m/s) and time taken = 15 (s)
dM1 substitutes: acceleration = 12 / 15
A1 0.80 m/s² cao
Answer: 0.80 m/s²

Question 10

M1 calculates acceleration for one interval, e.g. (3 - 0) / (2 - 0) = 1.5 m/s²
M1 calculates acceleration for a different interval, e.g. (9 - 6) / (6 - 4) = 1.5 m/s²
A1 both intervals (and the interval 4-6s to 2-4s, or overall) give the same value, 1.5 m/s², cao
B1 acceleration is constant because the velocity increases by equal amounts (3 m/s) in each equal time interval (2 s), oe
Answer: 1.5 m/s² (constant)

Question 11

M1 area of stage 1 (triangle) = 0.5 x 15 x 12 = 90 (m)
M1 area of stage 2 (rectangle) = 30 x 12 = 360 (m)
M1 area of stage 3 (triangle) = 0.5 x 6 x 12 = 36 (m)
A1 total distance = 90 + 360 + 36 = 486 m cao
B1 correctly identifies/uses that the area under a velocity-time graph gives the distance travelled
Answer: 486 m

Question 12

M1 change in velocity = 8.0 - 2.0 = 6.0 (m/s)
dM1 substitutes: a = 6.0 / 4.0
A1 1.5 m/s² cao
Answer: 1.5 m/s²

Question 13

M1 rearranges to make t the subject: t = (v - u) / a, oe
dM1 correct substitution with consistent signs, e.g. t = (0 - 6.0) / (-1.2), oe using magnitudes t = 6.0 / 1.2
A1 5.0 s cao
B1 correctly explains that the acceleration is negative (a deceleration) because Nia is slowing down, but the time taken must be positive, oe
Answer: 5.0 s

Question 14

B1 the two light gates are positioned at different, known points along the ramp
B1 as the interrupt card passes through each light gate, the data logger records the time taken for the card to cross that gate
B1 the trolley's velocity at each gate is calculated using velocity = length of card / time to cross the gate
B1 the data logger also records the time taken to travel between the two gates, and acceleration is then calculated using acceleration = change in velocity / time taken, using the two velocities and this time
Answer: Two light gates are set up at known points on the ramp; the interrupt card's crossing time at each gate gives a velocity (length of card / time), and the time between the gates lets these two velocities be used to calculate acceleration = change in velocity / time taken.

Question 15

(a) M1 substitutes: velocity = 0.050 / 0.125
(a) A1 0.40 m/s cao
(a) Answer: 0.40 m/s
(b) M1 substitutes: velocity = 0.050 / 0.050
(b) A1 1.0 m/s cao
(b) Answer: 1.0 m/s
(c) M1 ft substitutes: acceleration = (1.0 - 0.40) / 0.80, using their answers to (a) and (b)
(c) A1 0.75 m/s² cao (ft)
(c) Answer: 0.75 m/s²

Question 16

(a) B1 it reduces the effect of random error/any anomalous result, giving a mean value closer to the true acceleration, oe
(a) Answer: It reduces the effect of random error, giving a result closer to the true value.
(b) B1 use a shorter interrupt card
(b) B1 a shorter card takes less time to cross the light gate, so the trolley's velocity changes less while it is being measured, making the calculated velocity closer to the trolley's true (instantaneous) velocity at that point, oe
(b) Answer: Use a shorter interrupt card, so the measured velocity is closer to the trolley's instantaneous velocity at that point.

Question 17

M1 substitutes correctly: v² = (2.0)² + 2 x 1.5 x 6.0
A1 v² = 22 (m/s)² (4 + 18)
dM1 takes the square root of their v² value
A1 v = 4.7 m/s (2 s.f.), awrt 4.7
Answer: 4.7 m/s (2 s.f.)

Question 18

M1 rearranges v² = u² + 2as to make s the subject: s = (v² - u²) / (2a), oe
dM1 correct substitution with deceleration taken as negative: s = (0² - 24²) / (2 x (-3.0))
A1 s = 96 m cao
B1 obtains a positive distance despite the negative acceleration used, showing correct understanding of the sign convention
Answer: 96 m

Question 19

(a) M1 substitutes: a = (12 - 0) / 8.0
(a) A1 1.5 m/s² cao
(a) Answer: 1.5 m/s²
(b) M1 ft substitutes and rearranges: 12² = 0² + 2 x (their a) x s
(b) A1 48 m cao (ft)
(b) Answer: 48 m
(c) M1 ft calculates area of the triangle: 0.5 x 8.0 x 12 = 48 (m)
(c) B1 48 m matches the answer to part (b), so the two methods agree, oe
(c) Answer: 48 m; this agrees with part (b).

Question 20

Level 1 (1-2): One or two simple, isolated statements are made about the method, for example that it should be repeated, with little or no linkage between points and little reference to validity, accuracy or reproducibility.
Level 2 (3-4): A number of relevant points are made about the validity, accuracy or reproducibility of the method, showing some evidence of linkage, but the points may lack detail, or how to use the graph to reach a conclusion is not clearly addressed.
Level 3 (5-6): A detailed and coherent evaluation is given, covering validity, accuracy/precision and reproducibility, with clear links to the practical method, and a clear explanation of how the graph could be used to reach a valid conclusion. Relevant points are logically linked using appropriate scientific vocabulary.
Indicative content:
- control variables for a valid comparison, e.g. same trolley (same mass), same interrupt card length, same release point on the ramp and same distance between the light gates, for every height tested
- repeating each height three times and calculating a mean acceleration reduces the effect of random error/anomalous results, improving reliability
- checking for and repeating any anomalous results before calculating the mean
- using light gates rather than a stopwatch increases the accuracy of the velocity and time measurements, since it removes human reaction-time error
- testing a wide range of ramp heights, with small intervals between them, gives a more reliable picture of the relationship between height and acceleration
- to reach a valid conclusion, Aaliyah should plot acceleration (y-axis) against ramp height (x-axis), draw a line/curve of best fit, and use its shape/gradient to describe the relationship (e.g. whether acceleration increases in proportion to height)
- reproducibility could be checked by comparing her results with those from another group using different apparatus, to see if the same pattern is found

Motion: Speed, Velocity and Acceleration - Worksheets, Questions and Revision