Case 1: The car is pushed from rest to a speed of 1m/s over a distance of 5 m.
So the car is accelerated during this push.
KE of the car gained due to pushing = 1/2 m v² = 1/2 * 1000 kg * 1² (m/s)²
= 500 J
Work done against friction = friction force * displacement
= 500 N * 5 m = 2,500 J
Total work done in moving the car from rest to a speed of 1 m/s
= 2,500 + 500 = 3, 000 J
Case 2. The car is pushed at a uniform speed of 1 m/s over 5 m
Work done in moving the car is against the friction force.
W = F s = 500 N * 5 m = 2,500 J
Since the car is pushed at a uniform speed, the force exerted is equal to the friction force.