Constant Acceleration worksheets with answers

Introduces the language of motion (position, displacement, distance, velocity and speed) and how to find velocity from the gradient of a displacement–time graph. Students also work out average velocity and average speed for a journey, and convert between km h⁻¹ and m s⁻¹.

AQA 7357

P1, Q1, Q2

Edexcel 9MA0

6.1, 7.1, 7.2

Shows how to find acceleration from the gradient of a velocity–time graph and displacement from the area under it. Students learn how areas below the time axis affect displacement and distance, and sketch the matching displacement–time graph.

AQA 7357

Q1, Q2

Edexcel 9MA0

7.1, 7.2

Multi-stage journeys on velocity–time graphs: sketching the graph from a description and using the total area to find an unknown time or speed. Students also set up linked times and work out when two vehicles meet or one overtakes the other.

AQA 7357

Q1, Q2

Edexcel 9MA0

7.1, 7.2

Derives v = u + at and s = ½(u + v)t from the velocity–time graph. Students learn a clear routine (sketch, mark the positive direction, list s, u, v, a and t in SI units) and choose the formula from the letter they do not need, including deceleration and particles that turn round.

AQA 7357

P1, Q1, Q3

Edexcel 9MA0

6.1, 7.1, 7.3

Covers the three formulae you get by eliminating one letter: v² = u² + 2as, s = ut + ½at² and s = vt − ½at². Students practise choosing the right formula, solving a quadratic in t, and tackling problems over three points, including simultaneous equations.

AQA 7357

P1, Q1, Q3

Edexcel 9MA0

6.1, 7.1, 7.3

Explains what both roots of s = ut + ½at² mean, such as a particle passing the same point twice. Students find the time spent beyond a point and the total distance when a particle turns round, and work out where two particles meet when one starts later.

AQA 7357

Q1, Q3, B3

Edexcel 9MA0

7.1, 7.3, 2.3

Models an object moving up or down as a particle with constant acceleration g = 9.8 m s⁻², and the assumptions behind that model. Students find the greatest height, the time to the top, the time of flight and the landing speed, keeping one positive direction throughout.

AQA 7357

R3, Q3, OT3

Edexcel 9MA0

8.3, 7.3, OT3

Takes vertical motion further: how long an object stays above a given height, two objects moving on the same vertical line, and a bouncing ball treated as separate motions. Students also sketch and use the velocity–time graph for vertical motion.

AQA 7357

R3, Q2, Q3, OT3

Edexcel 9MA0

8.3, 7.2, 7.3, OT3

Mixed exam-style practice across the whole Constant Acceleration unit: graphs, the five constant-acceleration formulae and vertical motion under gravity. The focus is on choosing the right method before calculating, and keeping distance, displacement and signs straight.

AQA 7357

P1, Q1, Q2, Q3, R3, OT3

Edexcel 9MA0

6.1, 7.1, 7.2, 7.3, 8.3, OT3