Question

A motorist traveling at 15 m/s encounters a deer in the road 46 m ahead. If the maximum acceleration the vehicle’s brakes are capable of is −7 m/s 2 , what is the maximum reaction time of the motorist that will allow her or him to avoid hitting the deer?

Answer 1

2 seconds

Step-by-step explanation:

Acceleration = a = -7 m/s²

u = Initial velocity = 15 m/s

v = Final velocity = 0

Distance the car will travel after hitting the brakes = s

Distance to the deer = 46 m = s₁

Time it takes the car to stop = t

From equation of motion

`v^2-u^2=2as\\\Rightarrow (v^2-u^2)/(2a)=s\\\Rightarrow s=(0^2-15^2)/(2* -7)\\\Rightarrow s=(-225)/(-14)=16.07\ m`

`s_1-s=u\Delta t\\\Rightarrow \Delta t=(s_1-s)/(u)\\\Rightarrow \Delta t=(46-16.07)/(15)=1.99=2\ seconds`

Maximum reaction time would be 2 seconds.