A motorcyclist is attempting to accelerate to top speed and then immediately dec

Question

A motorcyclist is attempting to accelerate to top speed and then immediately decelerate to a stop in the shortest distance possible to create the largest skid marks. Starting from rest, he begins accelerating uniformly at a rate of 10 m/s^2 for a distance of 150 m. At this point, he is at maximum speed. At the 150 m mark, he slams on the brakes and begins decelerating uniformly at a rate of -14 m/s^2 until he comes to a complete stop.

a.) how much time has elapsed between when the motorcyclist began accelerating and when he reached his top speed.

b.) what is the cyclists top speed.

c.) how much time does it take the cyclist to come to a complete stop? (start counting from when he started braking.)

d.) how long are the cyclists skid marks? (assume he made skid marks the whole time he was braking)

Explanation / Answer

xf=1/2*a*t^2+vi*t 150=1/2*10*t^2 sqrt(150/5)=t=5.5 vf=at+vi vf=10*5.5=55 vf=at+vi 0=-14*t+55 t=55/14=3.93 vf^2=2ad+vi^2 0=2*-14*d+55^2 55^2/(28)=108=d

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