Question

A parent spots their young child running towards the road at a constant speed of 0.81 m s−1.

The parent is 12.8 m behind the child and the child is 5.6 m from the road.

The parent accelerates at a steady rate towards the child and the child is running directly away from the parent.

If the parent catches the child just as they reach the road then at what rate must the parent have accelerated?

Answer 1

The parent overcomes the distance

$12.8+5.6=18.4$ $m$

during $\frac{5.6}{0.81}=6.91$ $s$ .

The parent rate must be

$S=\frac{at^2}{2}\to a=\frac{2S}{t^2}=\frac{2\cdot18.4}{6.91^2}=0.77$ $\frac{m}{s^2}$