1. A go kart manufacturer is testing out a new model on a straight horizontal road.

Starting from rest, the velocity of the go kart is modelled by the equation 

$v=\frac{1}{w}{t}^{2}(60-t)$ 

where $vm{s}^{-1}$ is the velocity of the go kart at time $t$ seconds and $w$ is a constant.

Given the maximum speed of the go kart is $32{ms}^{-1}$, find the value of $w$ and the time at which the go kart reaches its maximum speed.