Question

A car accelerates uniformly from rest to 25/m/s/s in 10 seconds. Sketch the graph for displacement versus time graph

Answer 1

The displacement of the car is described by equation

$$d=v_it+\frac{at^2}{2}=\frac{at^2}{2}$$

The acceleration of the car

$$a=\frac{\Delta v}{\Delta t}=\frac{25\:\rm m/s-0\: m/s}{10\:\rm s}=2.5\:\rm m/s^2$$

So

$$d=\frac{2.5t^2}{2}=1.25t^2$$