A delivery Is travelling at a constant speed of 15m/s in a 60 km.h speed zone when the driver seems people walking across a pedestrian crossing 50m ahead of him.the driver takes exactly one second to react before he applies brakes as hard as he can.it takes a further 3 seconds for the van to a stop.will the van stop before the pedestrian crossing?show all calculations.

Question

A delivery Is travelling at a constant speed of 15m/s in a 60 km.h speed zone when the driver seems people  walking across a pedestrian crossing 50m ahead of him.the driver takes exactly one second to react before he applies  brakes as hard as he can.it takes a further 3 seconds for the van to a stop.will the van stop before the pedestrian crossing?show all calculations.

Steve · Answer

In one second he moves 15m, leaving 35m for braking.

The speed decreases from 15m/s to 0 in 3 seconds, meaning the acceleration

a = -15/3 = -5 m/s^2

Now, the distance traveled will be

s(t) = 15t - 5/2 t^2
So, is s(3) less than 35m?