Question

A 12 kg wagon is being pulled at an angle of 38degrees above horizontal. What force is applied to
the wagon if it accelerates from rest to a speed of 2.2 m/s over a distance of 3.4 m?
I not sure how to do this question. Is work involved for this question. I am completely stumped.

Answer 1

You can do it with work if you wish or you can do it with F = m a

with work

work done = Force in direction of motion * distance
Force in direction of motion = F cos 38
= .788 F
work done = .788 F * 3.4 meters
= 2.68 F Joules

that is the increase in kinetic energy
(1/2) m v^2 = .5*12 * 2.2^2
= 29 Joules
so
2.68 F = 29
F = 10.8 Newtons

Answer 2

with F = m a

f cos 38 = .788 F again

a = change in velocity/time
= 2.2/time
but time = distance/average speed
= 3.4 /1.1 = 3.09 seconds
so
a = 2.2/3.09 = .712 m/s^2
so
.788 F = 12 * .712
F = 10.8 Newtons (remarkable)