Mathematics 9709/42 — October/November 2021

The diagram shows a velocity-time graph which models the motion of a car. The graph consists of six straight line segments. The car accelerates from rest to a speed of $20\text{ m s}^{-1}$ over a period of $5\text{ s}$, and then travels at this speed for a further $20\text{ s}$. The car then decelerates to a speed of $6\text{ m s}^{-1}$ over a period of $5\text{ s}$. This speed is maintained for a further $(T - 30)\text{ s}$. The car then accelerates again to a speed of $20\text{ m s}^{-1}$ over a period of $(50 - T)\text{ s}$, before decelerating to rest over a period of $10\text{ s}$.