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

Answer:

2 seconds

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

$v^2-u^2=2as\\\Rightarrow \frac{v^2-u^2}{2a}=s\\\Rightarrow s=\frac{0^2-15^2}{2\times -7}\\\Rightarrow s=\frac{-225}{-14}=16.07\ m$

$s_1-s=u\Delta t\\\Rightarrow \Delta t=\frac{s_1-s}{u}\\\Rightarrow \Delta t=\frac{46-16.07}{15}=1.99=2\ seconds$

Maximum reaction time would be 2 seconds.