Two cars start from rest at a red stop light. When the light turns green, both c

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 4.4 m / s2 for 3.4 seconds. It then continues at a constant speed for 14.9 seconds, before applying the brakes such that the car's speed decreases uniformly coming to rest 280.13 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. 1.) How fast is the blue car going 1 seconds after it starts? 2.) How fast is the blue car going 8.8 seconds after it starts? 3.) How far does the blue car travel before its brakes are applied to slow down? 4.) What is the acceleration of the blue car once the brakes are applied? 5.) What is the total time the blue car is moving? 6.) What is the acceleration of the yellow car?

Explanation / Answer

1)after 1 sec

v=u+at=4.4*1=4.4 m/s

2)after 8.8 sec

velocity after 3.4 sec=4.4*3.4=14.96 m/s

so after 8.8 sec also,i will have same velocity=14.96 m/s

3)before brakes are applied

speed=14.96 m/s

4)accleration

distance travelled in 3.4 sec=0.5*a*t^2=25.432 m

distance travelled for next 14.9 sec=14.96*14.9=222.904

distance for stopping=(280.13-(222.904+25.432)=31.794 m

using v^2=u^2+2aS

v=0 m/s

a=-u^2/2S=-3.52 m/s^2

(5) total time=3.4+14.9+(14.96/3.52)=22.5 sec

(6)let accleration of yellow is a

280.13=0.5*a*22.5^2

a=1.1 m/s^2

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