Question

You are driving along the New York State Thruway in a line of cars all travelling at a constant speed of 108.5 km/hr. The car in front of you applies its brakes for maximum acceleration. You then apply your brakes to achieve the same maximum acceleration after only a 1 s delay due to reaction time. What distance behind the car in front of you must you be to avoid a collision?

Answer 1

Car first should be 30.13 m behind the second car.

Step-by-step explanation:

Given that,

Constant speed = 108.5 Km/hr

Time = 1 sec

Let the distance covered by second car S and by first car S'

We need to calculate the distance covered by second car

Using equation of motion

`S=ut-(1)/(2)at^2`.....(I)

The distance covered by first car to avoid collision

`S''=S'+S`

Put the value into the formula

`S'+S=ut+ut-(1)/(2)at^2`...(II)

We need to calculate the distance covered by first car

Using equation (I) and (II)

`S'=ut`

Put the value into the formula

`S'=108.5*(5)/(18)*1`

`S'=30.13\ m`

Hence, Car first should be 30.13 m behind the second car.