Question

A driver of a car going 90km/hr suddenly sees the lights of a barrier 40.0m ahead. It take the driver 0.75s before he applies the brakes (this is known as reaction time). Once he does begin to brake, he decelerates at a rate of 10m/s^2. Does he hit the barrier?

Answer 1

First, consider that the distance traveled by the car in 0.75s is:

`x=v\cdot t`

Convert 90km/h to m/s as follow:

Then, the distance x is:

`x=((25m)/(s))(0.75s)=18.75m`

Then, when the driver start to apply the brakes, the distance to the barrier is:

x' = 40.0 m - 18.75 m = 21.25 m

Next, calculate the distance that the car need to stop completely, by using the following formula:

`v^2=v^2_o-2ad`

where,

v: final velocity = 0m/s (the car stops)

vo: initial velocity = 25m/s

a: acceleration = 10m/s^2

d: distance = ?

Solve the previous equation for d and replace the values of the other parameters:

`d=(v^2_0-v^2)/(2a)=\frac{((25m)/(s))^2-((0m)/(s))^2}{2((10m)/(s))^{}}=31.25m`

Then, the drive needs 31.25 m to stop. If you compare the previous result with the distance of the car related to the barrier when the driver applies the brakes

(x' = 18.75 m), you can notice that d is greater than x'.

Hence, the car does hit the barrier.