Two cars start from rest at a red stop light.?

Question

Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 3.5 m/s2 for 4.3 seconds. It then continues at a constant speed for 7 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 172.33 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the blue car comes to a stop. It takes 137.3 meters for the blue car to travel before its brakes are applied.

What is the acceleration of the blue car once the brakes are applied? 

Thanks for helping!

peterpan · Accepted Answer

acceleration of blue car is given by
x=x0+v0t-1/2at^2
v=v0-at
when sopping v=0 and t=v0/a
replacing t into the first eq. on find
x0-x=v0^2/(2a)
and
a=v0^2/[2(x-x0)]
x0=137.30
x=172.33
x-x0=35.03
v0=at1=3.5*4.3=15.05 m/s
then
a=226.5/(2*35.03)=3.23 m/s^2  [module]

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Two cars start from rest at a red stop light.?

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