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 5.2 m/s2 for 4.5 seconds. It then continues at a constant speed for 13.1 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 428.16 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 3.6 seconds after it starts?

2)How fast is the blue car going 13.8 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.) time t = 3.6 s ; acceleration a = 5.2 m/s2 ; initial velocity u = 0 ;

v = u + at

v = 0 + 5.2 x 3.6 = 18.72 m/s

2.)At the end of time t1 = 4.5 s and with an acceleration a = 5.2 m/s2 the car gains speed v = 5.2 x 4.5 = 23.4 m/s

and remains constant for time 13.1 s.

time t =13.8 s;

now the blue car travels at constant speed v =23.4 m/s

3.) during time t1 = 4.5 s the blue car covers a distance s1 =ut +(1/2)at2 = 0.5 x 5.2 x( 4.5)2 = 52.65 m

during time t2 = 13.1 s the blue car covers a distance s2 = 23.4 x 13.1 = 306.54 m

so the total distance covered by blue car before its brakes are applied = 52.65 + 306.54 =359.19 m

4.) After brakes are applied ,

initial speed u = 23.4 m/s and final speed v = 0 m/s

distance travelled by blue car = 428.16 -359.19 = 68.97 m

v2 - u2 = 2as

a = -3.97 m/s2

5.) after brakes are applied , using v = u + at

time t3 = 23.4/3.97 = 5.89 s

so the total time the blue car is moving = t1 +t2 +t3 = 4.5 + 13.1 +5.89 =23.49 s

6.) distance travelled by yellow car s = 428.16 m

time t =23.49 s, initial velocity u =0;

using s=ut + (1/2) at2

acceleration of yellow car a = 1.55 m/s2   

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