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AS Mechanics · Edexcel 8MA0 · free A-level maths worksheet

Constant acceleration

The suvat equations in one dimension, choosing the right equation, multi-stage journeys.

12 original questions, 67 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

A car starts from rest and moves along a straight horizontal road with constant acceleration 2.5 m s−2.

Find

  1. the speed of the car after 6 s,
  2. the distance travelled by the car in the first 6 s.
3 marks
Show answer
a) 15 m s-1 b) 45 m
2

A cyclist moving along a straight road slows down with constant deceleration from 12 m s−1 to 4 m s−1 over a distance of 40 m.

Find

  1. the deceleration of the cyclist,
  2. the time taken to slow down.
4 marks
Show answer
a) 1.6 m s-2 b) 5 s
3

A van is travelling at 54 km h−1 along a straight road. It then accelerates uniformly at 1.2 m s−2 for 8 s.

  1. Find the speed of the van at the end of the 8 s, in km h−1.
  2. Find the distance travelled in the 8 s.
4 marks
Show answer
a) 88.6 km h-1 b) 158 m
4

A particle moves in a straight line with constant acceleration. It passes the point A with speed 4 m s−1 and the point B with speed 10 m s−1, where AB = 35 m.

  1. Find the acceleration of the particle.
  2. Find the time taken to travel from A to B.
  3. Find the speed of the particle as it passes the midpoint of AB.
6 marks
Show answer
a) 1.2 m s-2 b) 5 s c) 7.62 m s-1
5

A particle starts from rest and moves in a straight line with constant acceleration a m s−2. In the fifth second of its motion it travels 9 m.

  1. Find the value of a.
  2. Find the total distance travelled in the first 5 seconds.
4 marks
Show answer
a) a = 2 b) 25 m
6

A particle moves in a straight line with constant acceleration a. Its initial speed is u and after time t its speed is v and its displacement is s.

Starting from v = u + at and s = 12(u + v)t, show that v2 = u2 + 2as.

3 marks
Show answer
Eliminating t gives v2 = u2 + 2as
7

A car moves along a straight road with constant acceleration. It passes three signposts P, Q and R in that order, where PQ = QR = 48 m. The car takes 4 s to travel from P to Q and 2 s to travel from Q to R.

  1. Find the acceleration of the car.
  2. Find the speed of the car as it passes R.
7 marks
Show answer
a) 4 m s-2 b) 28 m s-1
8

A car starts from rest at a junction and accelerates uniformly at 1.5 m s−2 for 12 s. It then travels at constant speed for T seconds before decelerating uniformly at 2.25 m s−2 until it stops at a set of traffic lights. The total distance from the junction to the lights is 900 m.

  1. Find the greatest speed of the car.
  2. Find the value of T.
  3. Find the total time for the journey.
7 marks
Show answer
a) 18 m s-1 b) T = 40 c) 60 s
9

A lorry passes a point O on a straight road, moving with constant speed 20 m s−1. At the instant the lorry passes O, a car starts from rest at O and accelerates in the same direction with constant acceleration 2.5 m s−2.

  1. Find the time taken for the car to catch up with the lorry.
  2. Find the distance from O at which this happens.
  3. Find the speed of the car at this instant.
6 marks
Show answer
a) 16 s b) 320 m c) 40 m s-1
10

A particle P moves along a straight line. At time t = 0 it passes through a fixed point O with velocity 6 m s−1 in the positive direction. It has a constant acceleration of 2 m s−2 in the negative direction.

  1. Find the two times at which P is 5 m from O on the positive side.
  2. Find the greatest distance of P from O on the positive side.
  3. Find the total distance travelled by P in the first 7 s.
7 marks
Show answer
a) t = 1 s and t = 5 s b) 9 m c) 25 m
11

Two points A and B are 200 m apart on a straight road. A cyclist starts from rest at A and moves towards B with constant acceleration 1.2 m s−2. At the same instant a car passes B moving towards A at a constant speed of 15 m s−1.

  1. Find the time at which the cyclist and the car pass each other.
  2. Find the distance from A at which they pass.
  3. Find the speed of the cyclist at that instant.
7 marks
Show answer
a) 9.63 s b) 55.6 m c) 11.6 m s-1
12

A car passes a stationary police motorcycle at a constant speed of 25 m s−1 along a straight road. Two seconds later the motorcycle sets off after the car. It accelerates uniformly from rest at 4 m s−2 until it reaches its top speed of 35 m s−1, and then keeps this speed.

  1. Find the time taken for the motorcycle to reach its top speed, and the distance it covers in this time.
  2. Show that the motorcycle has not caught the car by the time it reaches its top speed.
  3. Find the time, measured from the moment the car passes the motorcycle, at which the motorcycle catches the car.
  4. Find the distance travelled by the car by then.
9 marks
Show answer
a) 8.75 s, 153 m b) at t = 10.75 s the car has gone 269 m, more than 153 m c) 22.3 s d) 558 m

Every question here is original and written by Robinson Tuition. It follows the Edexcel AS specification and suits AQA and OCR AS maths too; this is not an exam-board paper.

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