Question

derive the expression P=F×V​

Answer 1

Answer:

Power equal product of force and velocity. It is explined by simply by means of a example a toy dragged by a man by using some force apply on it. That cause car moves some distance to know power if applied force assumed as 1N that cause distance moved by car 1m in 1 sec then men acting 1 watt on it.

ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘꜱ ʏᴏᴜ. ☺❤

Answer 2

power = force x velocity

Power is defined as time derivative of the work done on a system.

Lets start with the definition of work:

W=∫r⃗ 2r⃗ 1F⃗ ⋅dr⃗ .

Now lets look at the definition of velocity:

v⃗ =dr⃗ dt

So, in the limit a dt→0 ,

v⃗ dt=dr⃗

If we let t0 be the time the system is at r⃗ 1 and t be the time the system is at r⃗ 2 , the integral for work becomes:

∫r⃗ 2r⃗ 1F⃗ ⋅dr⃗ =∫tt0F⃗ ⋅v⃗ dt′ .

Since P=dWdt , P=ddt∫tt0F⃗ ⋅v⃗ dt′ .

Using the fundamental theorem of calculus, we conclude that P=F⃗ ⋅v⃗ .