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

AI Thread Summary
The discussion revolves around calculating the stopping distance of a car after the driver's reaction time when encountering an obstacle. The car, traveling at 100 km/h, covers approximately 41.66 meters during the driver's 1.5-second reaction time, leaving 78.34 meters for braking. With a steady deceleration of 7.5 m/s², the car takes about 3.70 seconds to stop, covering 51.41 meters during braking. This results in a final distance of 27 meters from the elk after the car has stopped. The calculations confirm the stopping distance, and the discussion highlights the use of different equations to arrive at the same conclusion.
chawki
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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.
 
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so what is your question?
 
It is fine, but why have you calculated the time?

ehild
 
i was going to use the equation x=1/2 *a*t2+V0*t+x0
 
you have got your answer anyways.
 
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