A-level · Kinematics

Motion graphs (displacement–time & velocity–time)Exam-style questions

What the gradient and the area mean on each kind of motion graph — gradient of displacement–time is velocity, gradient of velocity–time is acceleration, area under velocity–time is displacement — and how to model a journey as a graph and read unknowns off its area.

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

DifficultyAllLevel 3Level 4Level 5
  1. 1
    The velocity-time graph shows a particle's motion. Find the total distance travelled.246810125101520t (s)v (m/s)
    Level 3 · 2 marksTry it
  2. 2
    A velocity-time graph shows a particle accelerating uniformly from rest to 20 m s−120\ \text{m s}^{-1} in 44 s. Find the acceleration.
    Level 3 · 2 marksTry it
  3. 3
    The velocity-time graph shows a particle's journey. Find
    (a) the total distance travelled and (b) the average speed.510152051015t (s)v (m/s)
    Level 3 · 3 marksTry it
  4. 4
    A particle decelerates uniformly from 18 m s−118\ \text{m s}^{-1} to 6 m s−16\ \text{m s}^{-1} in 33 s. Find the deceleration (the magnitude of the gradient of the velocity-time graph).
    Level 3 · 2 marksTry it
  5. 5
    On a velocity-time graph a particle travels at a constant 12 m s−112\ \text{m s}^{-1} for 88 s, then decelerates to rest in a further 44 s. Find the total distance travelled.
    Level 3 · 2 marksTry it

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