Question

A truck is stopped at a stoplight. When the light turns green, the truck accelerates at 3.0 m/s2. At the same instant, a car passes the truck going 12 m/s. Where and when does the truck catch up with the car?

Answer 1

The truck's position at time $t$ is

$x_{\rm truck}=\dfrac12\left(3.0\dfrac{\rm m}{\mathrm s^2}\right)t^2$

and the car's position is

$x_{\rm car}=\left(12\dfrac{\rm m}{\rm s}\right)t$

The two vehicle's meet when their positions are the same, at which point

$\dfrac12\left(3.0\dfrac{\rm m}{\mathrm s^2}\right)t^2=\left(12\dfrac{\rm m}{\rm s}\right)t$

$\implies\left(1.5\dfrac{\rm m}{\mathrm s^2}\right)t\left(t-8\,\mathrm s\right)=0$

$\implies\boxed{t=8.0\,\mathrm s}$