Since we know the initial and final velocities and the constant mass we can find the initial and final momenta of the object and therefore the change in momentum.

• The initial momentum is m v0 = 8 kg * 8 m/s = 64 kg m/s.
• The final momentum is m vf = 8 kg * 3.02 m/s = 24.16 kg m/s.
• The change in momentum is therefore 24.16 kg m/s - 64 kg m/s = - 39.84 kg m/s.

From the change in momentum and the time interval we easily calculate the average force:

• We use p to stand for momentum; change in momentum is thus designated `dp and the Impulse-Momentum Theorem says that `dp = Fave `dt.
• It follows from our previous calculation of momentum change that Fave = `dp / `dt.
• Thus we obtain the desired average force:

• Fave = `dp / `dt = =- 39.84 kg m/s / ( .3 sec) = - 132.8 Newtons.

Here we have implicitly chosen the direction of motion as the positive direction.   The negative force indicates that the force is in the negative direction--i.e., the direction opposite that of the motion.  This is what we would expect, since the object is slowing down.

We know from the Impulse-Momentum Theorem that the change in momentum `dp is equal to the product Fave `dt.

• If we know `dt and can find the change `dp in momentum we can then easily find Fave: Fave = `dp / `dt.

In this case we know the constant mass m of the object and its initial and final velocities v0 and vf.

• We can therefore calculate the initial and final momenta: p0 = m v0 and pf = m vf.
• The change in momentum is therefore `dp = pf - p0 = m vf - m v0.
• It follows that the average force is

• Fave = `dp / `dt = ( m vf - m v0 ) / `dt.