Question

give mathematical relationship between power force and velocity Express kilowatt in terms of Joule per second​

Answer 1

Answer: P= F·v

Here, P is the power, F is the force vector and v is the velocity vector.

Explanation:

Power, by definition, is the rate of doing work/delivering energy, i.e.

$P=\frac{dW}{dt}$ -----(1)

Further, work is defined as the dot product of Force vector and displacement vector, i.e.

W = F·r ----(2)

,where r represents the displacement vector.

From (1) and (2),

$P=\frac{d}{dt} (F.r)$

For a constant force F,

$P=F.\frac{dr}{dt} =F.v$

which is the required result.(Apologies for the formatting; the correct relation is denoted by the scalar product P=F·v)

1 kilowatt = 1000 Watt = 1000 Joule/Second