Question

a car drives along the straight level frictionless road by an engine delivering constant power. how is velocity of car related to time elapsed?

Answer 1

power is given by f.v
where f is force and v is velocity of particle
power =k
mav=k
m(dv/dt)v=k
mdv x v= kdt
integrating both sides
mv^2=kt
v is directly proportional to√t

Answer 2

Answer:

The velocity of the car is related to the square root of time elapsed.

Explanation:

The relation between power and velocity is given as,

$P=F.v$         (1)

Where,

P=power delivered by the engine

F=force acting

v=velocity with which the car is moving

Also,

$F=m\frac{dv}{dt}$         (2)

m=mass of the body

dv=change in velocity

dt=change in time

By substituting equation (2) in equation (1) we get;

$P=m\frac{dv}{dt} .v$

$Pdt=mv\frac{dv}{dt}$

On integrating both sides,

$\int Pdt=m\int v\frac{dv}{dt}$

$Pt=\frac{mv^2}{2}$      (3)

From equation (3) we get;

$v\propto\sqrt{t}$

Hence, the velocity of the car is related to the square root of time elapsed.