Question

derive the formula f=mv/t​

Answer 1

Newton's 2nd Law tells us that force = mass x acceleration ( F = ma ). Since acceleration is just how velocity changes over time, we can write this as  

F = m * v/t  

Multiply both sides by time to arrive at  

F t = m v  

Since mv is momentum, we can see that the momentum conferred to an object by a force equals the force times the time the force is applied. Thus if a 15 Newton force to the right is applied to an initially stationary object for 3 seconds, it will have a momentum of 45 kg m/s to the right.  

Most students who ask this question are usually trying to figure out the reverse situation, however. If an object hits me with a certain amount of momentum, how much force does it hit me with? Note that due to Newton's 3rd Law, this can be calculated the same way. If a thrown egg hits your hand with a momentum of 5 kg m/s, the force it applies to your hand depends on the time it takes for your hand to absorb the momentum. If you hold your hand very stiffly (and try to make the egg stop in a very short period of time) the ball exerts a high force on your hand, e.g. 100 N for 1/20th of a second. However as anyone who has ever played in an egg toss knows, if you let your hand 'give' and extend the amount of time it takes to absorb the momentum, the egg exerts a smaller force on your hand.

Answer 2

$\textbf{\huge{ANSWER:}}$

Let's start from the Newton's Second Law Of Motion. The Newton's Second Law Of Motion is :-

The Rate of change of momentum in a moving body is directly proportional to the applied unbalanced Force in the direction of motion.

So, by this, we get :-

Change in momentum = $p_{2} - p_{1}$

We know that :- p = mv ( momentum = mass × velocity )

Expand it further =》 $mv - mu$

Now, it given rate of momentum. So,

Rate of momentum = $\frac{mv - mu}{t}$

Therefore, we get :-

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

Now, when :-

u = 0 m/s ( That means that the object has started from the rest position )

F = $\frac{mv}{t}$

$\boxed{\tt{Hence\:Proved!}}$