Question

A mechanic pushes a 2520 kg car from rest
to a speed of
v
, doing 4310 J of work in the
process. During this time, the car moves
22.4 m.
Find the speed
v
. Neglect friction between
car and road. Answer in units of m/s.

Answer 1

change of momentum = 2520 v

average force = change of momentum/time
F = 2520 v/t
work = force * distance
4310 = 2520 v/t * 22.4
or
v/t = .0764 or t = v/.0764

now if force were constant
d = (1/2) a t^2
44.8 = a t^2
v = a t so a = v/t
so
44.8 = v t = v^2/.0764
v^2 = 3.42
v = 1.85 m/s

Answer 2

easier way
work done = final (1/2) m v^2
4310 = (1/2)2520 v^2
v = 1.85 m/s ;)