Question

A car of mass 1200 kg starts from rest, accelerates uniformly to a speed of 4.0 m/s in 2.0 s and continues moving at this constant speed in a
horizontal straight line for an additional 10 s. The brakes are then applied and the car is brought to rest in 4.0 s. A constant resistance
force of 500 N is acting on the car during its entire motion.
Calculate the force accelerating the car in the first 2.0 s of the motion.

Answer 1

phase 1:
av speed = 4/2 = 2 m/s
x = 0 + 2 t = 4 meters

phase 2
v = 4 m/s
x = 4 + 10*4 = 4 + 40

phase 3
Vi = 4 m/s
Xi = 44
average v = 2
x = 44 + 2*4 = 52 meters total

work done by resistance during phase 1 = 500 N * 4 meters =2000 Joules
kinetic energy gained during phase 1
=(1/2)1200 (4^2) = 9600 Joules
so total energy input during phase 1
= 11,600 Joules

That is force * distance
and distance = 4 meters