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 5.8 m/s2 for 3.3 seconds. It then continues at a constant speed for 9.3 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 244.01 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 far does the blue car travel before its brakes are applied to slow down?

2)What is the acceleration of the blue car once the brakes are applied?

3)What is the total time the blue car is moving?

4)What is the acceleration of the yellow car?

Explanation / Answer

blue car journey:
a) when it starts and accelerates for 3.3 s
   a_b = 5.8m/s^2
   initial speed u = 0
   distance covered S1 = ut + 0.5 at^2 = 0 + 5.8*3.3^2 = 31.581 m
b) when blue car continues at a constant speed for 9.3 seconds:
   velocity at start of this phase ,v_b = u +at = 0+ 5.8 *3.3 = 19.14 m/s
   distance covered during constant velocity S2 = v_b * 9.3 = 19.14*9.3=178.002 m
  
c) blue car applies brake and comes to rest 244.01 meters from where it started
distance covered while braking S3 = 244.01 - (31.581 + 178.002) = 34.427 m
for this phase initial speed was v_b = 19.14 m/s
and final speed = 0
so 0^2 - 19.14^2 = 2 A (S3)
A = - 19.14^2 / (2*34.427) = -5.32m/s^2
time taken t_3:
0 = 19.14 -5.32*t_3
t_3 = 3.597 s
hence total time blue car is moving = 3.3 + 9.3 + 3.597 = 16.197 s
yellow car case:
The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the blue car comes to a stop
time of trip for yellow car = same as blue car for entire trip = 16.197 s
distance covered = 244.01 m
using relation :
S = ut +0.5 at^2
244.01 = 0 + 0.5 a *16.197^2
a = 1.86 m/s^2
-----------------------------
1)How far does the blue car travel before its brakes are applied to slow down? (ans 34.427 m)
2)What is the acceleration of the blue car once the brakes are applied?(ans -5.32m/s^2)
3)What is the total time the blue car is moving? (ans 16.197)
4)What is the acceleration of the yellow car? (ans 1.86 m/s^2)

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