What is the Stopping Distance of a Car After Reaction Time?

[chawki]

Homework Statement

The car velocity is 100 km/h. Suddenly, the driver sees a elk 120 m from the car standing on
the road. The driver’s reaction time is 1,5 s, after which time the driver starts braking. The
braking is assumed steady and the deceleration is 7,5 m/s². The car stops in 4 s.

Homework Equations

Calculate the distance between the standing elk and the car after the car has stopped. Give the answer in 1m precision.

The Attempt at a Solution

At his reaction time, he traveled 27.77*1.5 = 41.655 m
so the distance left for braking is 120-41.655 = 78.345m

V = a*t +V₀
t = (V-V₀)/a
t = (0-27.77)/-7.5
t = 3.702 s and that's the time for coming to a stop.

V²-V₀² = 2*a*x
x=51.41m
so he stopped after 51.41m of braking, and that's 78.345-51.41 = 26.935 from the elk
In 1m precision it would be 27m.

 

[supratim1]

so what is your question?

 

[ehild]

It is fine, but why have you calculated the time?

ehild

 

[chawki]

i was going to use the equation x=1/2 *a*t²+V₀*t+x₀

 

[supratim1]

you have got your answer anyways.