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 4.9 m/s2 for 4.1 seconds. It then continues at a constant speed for 10.5 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 290.43 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 1.6 seconds after it starts? the anwser is 7.84

2)How fast is the blue car going 8 seconds after it starts? the anwser is 20

3)How far does the blue car travel before its brakes are applied to slow down? ( the anwser is not 260.6 not 101.1 not 82.32) help plz

4)What is the acceleration of the blue car once the brakes are applied? ( the anwser is not -7.39 not 7.4 and not 5 .1) help plz

5)What is the total time the blue car is moving? help plz

6)What is the acceleration of the yellow car? help plz

Explanation / Answer

1) The blue car is going 1.6 seconds after it starts

velocity = 1.6 * 4.9 = 7.84 m/s

2) The blue car is going 8 seconds after it starts means velocity at the end of the first 4.1 sec

Velocity = 4.1*4.9 = 20 m/s

3) Distance coverd in the first 4.1 sec

D1 = [4.9 * (4.1)^2 ]/2 = 41.18m

Distance covered during the second part

D2 = 20.09 * 10.5 = 210.9,m

now D1 + D2 = 252.08 m

3) Acceleration in the third part

0 =(20.09)^2+2*a*38.30

a = -5.26 m/sec^2

5) Calculate the time for third part

38.30 = 20.09*t/2

t= 3.812 sec

Calculate the total time

T =4.1 +10.5 +38.1 = 18.4 sec

6) The acceleration of the yellow car

290.43 = a (18.4)^2/2

a = 1.71 m/s^2

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