Question

derive the relation between acceleration and rate of momentum

Answer 1

Explanation:

Knowing the amount of force and the length of time that force is applied to an object will tell you the resulting change in its momentum. They are related by the fact that force is the rate at which momentum changes with respect to time (F = dp/dt). Note that if p = mv and m is constant, then F = dp/dt = m*dv/dt = ma.

Answer 2

Explanation:

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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.

$\tt \: F=kmv− \frac{mu}{t} \\ \\ </p><p></p><p> \tt \: F= \frac{km(v \: u)}{t}$

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

$\tt \: v− \frac{u}{t} = a$

$\tt \: Hence F=kma \\ </p><p></p><p> \tt \: But k=1 \\ </p><p></p><p> \tt \: Hence F=ma$

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

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.

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