Question

You’re driving down the highway late one night at 20m/s when a deer steps onto the road 85m in front of you. Your reaction time before stepping on the brakes is 0.50s, and the maximum deceleration of your car is 9m/s2. From the time you first see the deer until your car comes to a complete stop, how far have you travelled?

Answer 1

The car travels to a complete stop from the time the deer is first seen and the distance traveled is 10.04 m.

Step-by-step explanation:

The speed of the car is 20 m/s.

The deer that steps on to the road is 85 m in front of the car.

Seeing the deer the brakes are applied but after a reaction time of 0.5 seconds.

The deceleration of the car is given as 9 m/
`s^2`.

The formula for distance is given as

`s = ut + (1)/(2) at^2` .... (i)

where s = distance traveled in meters

u = initial velocity

a = acceleration

t = time

and v = u + at .... (ii)

where v = final velocity

u = initial velocity

a = acceleration

t = time in seconds

Therefore we have from (ii) 0 = 20 - 9t

Therefore time it takes for the car to stop, t =
`(20)/(9)` = 2.22 seconds.

Therefore from (i) we have

s = 20(t + 0.5) - 9
`t^2`

= 20(2.22 + 0.5) - (9 ×
`2.22^2`)

= 54.4 - 44.36

= 10.04 m

In the above distance formula that is also mentioned in (i) we have accounted for the reaction time which is 0.5 seconds.

The car travels to a complete stop from the time the deer is first seen and the distance traveled is 10.04 m.