A 4.4g bullet leaves the muzzle of a rifle with a speed of 322 m/s. What total constant force is exerted on the bullet while it is traveling...

To solve this problem, we use the Work-Energy Theorem

Work = change in Kinetic Energy

where Work is

W = F d

and Kinetic Energy is

KE = 1/2 m v^2

The initial KE of the bullet is zero, so the change in KE is found using the mass and final velocity of the bullet. We know the distance over which the force is applied, so the average force on the bullet over that distance is found from

F d = 1/2 m v^2

F = ( 1/2 m v^2 ) / d

F = ( 1/2 ) ( .0044 kg ) ( 322 m/s )^2 / ( .75 m )

F = 304 kg m/s^2

The average force exerted on the bullet is 304 Newtons.

If you have not yet studied the Work-Energy Theorem, the problem can also be solved using kinematics. We can find the acceleration of the bullet using the equation

2 a d = v^2

where a is the acceleration, d the distance traveled, and v the final velocity. Once we have the acceleration, Newton's Second Law gives us the force:

F = m a

where m is the mass of the bullet (in kilograms) and a the acceleration we just found.