Answer to Question #96688 in Mechanics | Relativity for Mark Sekla

Question

Two boys are racing for chocolates. The older one has a speed of 1.0 m/s and the younger one has a 0.50 m/s. The older one told the younger one to run first, which the younger one does. Ten seconds later the older one follows. How far would they be from the starting line for the older one to overtake the younger one.

Answer 1

The equations of motion of boys

$$x_{\rm younger}(t)=0.50t+5$$

$$x_{\rm older}(t)=1.00t$$

When boys will meet

$$x_{\rm younger}(t)=x_{\rm older}(t)$$

$$0.50t+5=1.00t$$

$$t=10\:\rm s$$

The distance of the boys from starting point

$$d=x_{\rm younger}(10\:{\rm s})=x_{\rm older}(10\:\rm s)=10\:\rm m$$