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

`t = 1.29 s`

Step-by-step 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 = (x)/(v)`

`t = (21.9)/(17)`

`t = 1.29 s`