Question

What is the initial velocity of a go-kart traveling at a uniform acceleration of 0.5 m/s^2 for 5s as it slows down to a stop?

Answer 1

The go-kart's velocity $v$ after time $t$ is given by

$v=v_0+at$

where $v_0$ is its initial velocity and $a$ is its acceleration. After $t=5\,\mathrm s$, the go-kart stops completely, so

$0\,\dfrac{\mathrm m}{\mathrm s}=v_0+\left(-0.5\,\dfrac{\mathrm m}{\mathrm s^2}\right)(5\,\mathrm s)\implies v_0=2.5\,\dfrac{\mathrm m}{\mathrm s}$

where $a<0$ because we know the go-kart is slowing down.