Aforce in the negative direction of an x axis is applied for 34 ms to a 0.40 kg ball initially moving at 16 m/s in the positive direction of the axis. the force varies in magnitude, and the impulse has magnitude 32.4 n·s.(a) what is the ball's speed just after the force is /s(b) what is the average magnitude of the

(a) 96 m/s

The impulse theorem states that the impulse exerted on the ball is equal to the change in momentum of the ball:

where

is the impulse exerted on the ball

is the mass of the ball

is the final speed of the ball

is the initial speed of the ball

Solving the equation for v, we find

(b) 952.9 N

The impulse is also equal to the product between the average force and the contact time:

where here we have

is the impulse

is the average force

is the contact time

Solving the equation for F, we find the force: