Question

Show that the rate of change of momentum = mass × acceleration. Under what condition does this relation hold?

Answer 1

Let a force 'F' be applied on a body of mass m for a time 't' due to which its velocity changes from u to v. Then,

Initial momentum of body = mu

Final momentum of body = mv

Change in momentum of the body in 't' seconds = mv -­­ mu = m (v - u)

Rate of change of momentum = Change in momentum/time

  = [m (v - u)]/t

However, acceleration a = Change in velocity/time = (v - u)/t

Therefore, rate of change of momentum = ma = mass × acceleration

This relation holds true when the mass of the body remains constant.

Answer 2

According to newton second law
F = m X a
a= (v - u)/t.
F = m(v -u)/t
F = (mv - mu)/t
As F= m X a
ma = (mv - mu)/t
so rate of change of momentum = mass X acceleration.
This relation holds good when mass remains constant during motion.