A-level · Kinematics

Kinematics with calculus (a → v → s)Exam-style questions

Why integrating acceleration gives velocity and integrating velocity gives displacement, where the suvat formulas actually come from, and why they silently break the moment acceleration varies.

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22 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
A particle moves in a straight line with acceleration $a = (6t - 4)\ \text{m s}^{-2}$ . At $t = 0$ its velocity is $2\ \text{m s}^{-1}$ .
(a) Find an expression for the velocity at time $t$ . (3 marks)
(b) Find the velocity when $t = 2$ . (1 mark)
Level 3 · 4 marksTry it
2
A particle moves in a straight line with velocity $v = (2t + 3)\ \text{m s}^{-1}$ . At $t = 0$ its displacement from a fixed point $O$ is $5\text{ m}$ .
(a) Find an expression for the displacement from $O$ at time $t$ . (3 marks)
(b) Find the displacement when $t = 4$ . (1 mark)
Level 3 · 4 marksTry it
3
A particle moves in a straight line with velocity $v = (t^{2} - 5t + 6)\ \text{m s}^{-1}$ at time $t$ seconds.
(a) Find the times at which the particle is instantaneously at rest. (2 marks)
(b) Find the displacement of the particle from its starting point when $t = 4$ . (3 marks)
(c) Find the total distance travelled between $t = 0$ and $t = 4$ . (4 marks)
Level 3 · 9 marksTry it
4
A particle moves in a straight line with velocity $v = \dfrac{12}{(t + 1)^{2}}\ \text{m s}^{-1}$ at time $t$ seconds.
(a) Find the acceleration when $t = 1$ . (3 marks)
(b) Find the distance travelled between $t = 0$ and $t = 1$ . (3 marks)
Level 3 · 6 marksTry it
5
A particle moves in a straight line with velocity $v = (12t - 3t^{2})\ \text{m s}^{-1}$ at time $t$ seconds.

Find the maximum velocity of the particle. (4 marks)
Level 3 · 4 marksTry it

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