MathsYears 12–13Mechanics

Variable acceleration

Use calculus for kinematics with variable acceleration; differentiate and integrate displacement, velocity and acceleration

What you'll learn

  1. 1

    Imagine a car speeding up or slowing down — that's variable acceleration!

  2. 2

    Here's a speed-time graph for a car. The curve shows speed changing at different rates.

  3. 3

    Find the acceleration at t=2s for v = 3t² + 2t + 1.

  4. 4

    Drag the point on the speed-time graph to see how acceleration changes.

  5. 5

    What is the acceleration when v = t³ at t=1? (Hint: differentiate first)

  6. 6

    Find when acceleration is zero for v = 2t³ - 12t² + 18t.

  7. 7

    For v = t² - 4t + 5, what is the acceleration at t=2?

Practise Variable acceleration with Whizlo

Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 16–18. Aligned to the UK National Curriculum.

Start free →Sign in