Find momentum given a motion equation

Question

Given a motion equation x=5-8t+4t², and the object of 2 kg mass, find its momentum after 2 s and 4 s. What is the average force?

Answers: 16 kg*m/s, 48 kg*m/s, 16 N

Answer 1

This question has the answers given already.

Perhaps what is wanted is the method.

Momentum is mass times velocity.

p = m v

Velocity is the first derivative of position with respect to time:

v = x' = dx/dt

v = -8 + 8t

v at 2s = -8 + 16 = 8 m/s

v at 4s = -8 + 32 = 24 m/s

Get the momentum by multiplying by m = 2 kg

giving p = 16 and 48 kg-m/s.

Acceleration is the change in velocity per unit time,

so the average acceleration is

a = (24 - 8) / 2 = 8 m/sec^2

Can also get the acceleration by differentiating the velocity with respect to time:

a = v' = x" = 8

and here a is constant.

Force is mass times acceleration,

f = m a = 2*8 = 16 N in SI units