Question

A motorist traveling at 17 m/s encounters a deer in the road 46 m ahead. If the maximum acceleration the vehicle’s brakes are capable of is −6 m/s 2 , what is the maximum reaction time of the motorist that will allow her or him to avoid hitting the deer? Answer in units of s.

Answer 1

Answer:

$t = 1.29 s$

Explanation:

Maximum distance after which the motorist must have to stop is given as

$d = 46 m$

now the distance after which the vehicle will stop on applying breaks is given as

$v_f^2 - v_i^2 = 2 a d$

$0 - 17^2 = 2(-6) d$

$d = 24.1 m$

now remaining distance is given as

$x = 46 - 24.1$

$x = 21.9 m$

now reaction time is given as

$t = \frac{x}{v}$

$t = \frac{21.9}{17}$

$t = 1.29 s$