Question

Show that rate of change of momentum= mass \times acceleration.Under what condition does this relation hold

Answer 1

Force can also be called the change in momentum.

Based on the assumption that there is not any external force that is acting right on the system, the overall change in momentum is directly proportional to the force applied.

$F=kmv-\frac{mu}{t}$

$F=\frac{km(v-u)}{t}$

$F=km(v-\frac{u}{t})$

$v-\frac{u}{t}=a$

Hence $F=kma$

But $k=1$

Hence $F=ma$

And so since $ma=m(v-\frac{u}{t})$

Then the time rate of change of momentum is equal to the product of mass and acceleration.

Based on all of this, it is clear that rate of change of momentum = mass x acceleration.

This holds true when there is no external force acting on the system.