Question

A car starts from rest and has an acceleration a=t . A truck is moving with a uniform velocity of 6 m/s. At what distance will the car overtake the truck . (At t=0 both start their motion the same direction form the same position.

Answer 1

$$\begin{gathered} Thedis\tan cetravelledbycarintimetisgivenby; \\ s=\frac{1}{2}a{t}^2=\frac{1}{2}t\times t^2=\frac{1}{2}{t}^3 \\ anddis\tan cetravelledbytruckintimetis \\ s=ut=6\times t \\ Therefore\frac{1}{2}{t}^3=6\times t \\ or{t}^2=12 \\ ort=2\sqrt{3} \\ Thereforedis\tan cecoveredbycarinovertakingthetruckis \\ s=6\times 2\sqrt{3}=12\sqrt{3}=12\times 1.732=20.784m \end{gathered}$$