Question

Prove that:
a) Force = ma
b) Momentum = mv

Answer 1

a) Newton’s 2nd law of motion which states that the net force acting on a system is directly proportional to rate of change of momentum of the system.

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Or, Force = mass × acceleration

b) P = Momentum, m = mass, v = velocity. We know, momentum is the quantity of motion produced in a body. 
This implies, if two bodies are of equal mass, but different velocity, then the amount of motion is greater in the body moving with greater velocity. Momentum = motion, to put it simply. Thus, motion of a fast body > motion of a slow body. So, momentum is directly proportional to velocity. 

Also, if two bodies are traveling with equal velocity, the one of larger mass will have larger inertia of motion, so it will try to sustain its state of motion more than the other. Hence, we can easily say that it has large motion as it will be difficult to stop it.

Thus, momentum is directly proportional to mass also.
 
Momentum = mass x velocity [proved].

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