How to derive ${\bf \vec{F}} = \dfrac{m(v_f - v_i)}{t}$ or ${\rm \vec{F}} \propto \dfrac{m(v_f - v_i)}{t}$, for that matter?

Note, you do not have to use ${\bf \vec{F}} = m{\bf \vec{a}}$

Question

How to derive ${\bf \vec{F}} = \dfrac{m(v_f - v_i)}{t}$ or ${\rm  \vec{F}} \propto \dfrac{m(v_f - v_i)}{t}$, for that matter?

Note, you do not have to use ${\bf \vec{F}} = m{\bf \vec{a}}$

parthkohli · Answer

@amistre64

dls · Answer

$$\LARGE F=\frac{dp}{dt}$$
Can we use this? :P

parthkohli · Answer

Good idea! ^_^

No.

amistre64 · Answer

force is equal to change in momentum divided by change in time

dls · Answer

-_- @ParthKohli

parthkohli · Answer

@amistre64 Isn't that just what DLS said...

amistre64 · Answer

i was just seeing if i remembered how to interpret the question correctly :)

parthkohli · Answer

$$F = \dfrac{\Delta p}{\Delta t} = \dfrac{\Delta mv}{\Delta t}$$Is the above true? How did you derive it?

amistre64 · Answer

Ft = p = mv2-mv1

amistre64 · Answer

$$\vec F\Delta t=\Delta \vec p = m(\vec v_f-\vec v_i)$$

amistre64 · Answer

not sure what you mean by how you derive it.

parthkohli · Answer

Does not seem so convincing. :-|

amistre64 · Answer

do we have to first prove that momentum is a product of mass and velocity?  i never know when i have to reinvent the wheel on these things

parthkohli · Answer

No, not that one. lol, got it

amistre64 · Answer

changing an objects momentum requires applying a force over a given interval of time, right?$$\vec F\Delta t=\Delta \vec p$$

parthkohli · Answer

I'd rather say...$$\vec F \Delta t \propto \Delta \vec p$$

amistre64 · Answer

that style went out with Descartes :)

parthkohli · Answer

I feel like a newbie here!

parthkohli · Answer

Can you give me a link to the derivation? I got how you mean $\Delta \vec p =m(\vec v _f - \vec v_i)$ and there's only a little work left... but I didn't get how $\vec F \Delta t = \Delta \vec p  $.

dls · Answer

You are indirectly asking for the proof of F=ma which only Isaac Newton knows.

dls · Answer

I think @shubhamsrg can derive F=ma.
Its a piece of cake for him.

parthkohli · Answer

Of course, of course!

amistre64 · Answer

an object remains at a constant velocity (change in velocity is acceleration) unless acted upon by a force.

therefore in order to change an objects momentum, you would need to apply a constant force

amistre64 · Answer

over a given time interval, the mass "acquires" a new velocity, and therefore a change in momentum.  does that sound about right?