a)Your are standing with your 1,058-kg car at a red light. The light turns green

Question

a)Your are standing with your 1,058-kg car at a red light. The light turns green, and you speed up your car to 61 mph. What is the total work done on your car?

b)Your are driving your 1,058-kg car at a speed of 61 mph. A traffic light in front of you turns red and you bring your car to a complete stop. What is the total work done on your car?

c)Your are standing with your 1,150-kg car at a red light. The light turns green, and you speed up your car to 29 mph. Then you continue at a constant speed. After another mile, what is the total work done on your car from the moment you started from rest?

Explanation / Answer

The change in the kinetic energy of an object is equal to the net work done on the object.
(a)
Vin = 0 , (At Standing Position)
Vfi = 61 mph = 27.3 m/s

K.E in = (1/2)*m*v^2
K.E in = 0

K.E fin = (1/2)*m*v^2
K.E fin = (1/2)*1058*27.3^2
K.E fin =  3.94 * 10^5 J

Wnet = K.E fin - K.E in
Wnet = 3.94 * 10^5 J

(b)
Vin = 61 mph = 27.3 m/s
Vfi = 0 , (At Stop Position)

K.E in = (1/2)*m*v^2
K.E in = (1/2)*1058*27.3^2
K.E in = 3.94 * 10^5 J

K.E fin = (1/2)*m*v^2
K.E fin = 0 (As v = 0 , at Standing Position)

Wnet = K.E fin - K.E in
Wnet = - 3.94 * 10^5 J

(c)
Vin = 0 , (At Standing Position)
Vfi = 29 mph = 13 m/s

K.E in = (1/2)*m*v^2
K.E in = 0

K.E fin = (1/2)*m*v^2
K.E fin = (1/2)*1150 *13^2
K.E fin =  97175 J

For Constant Velocity stretch, No work is done as Force = 0.

Wnet = K.E fin - K.E in
Wnet = 97175 J

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