Question

A body is initially at rest. It undergoes one dimensional motion with constant acceleration. the power delivered to it at time t is proportional to

Answer 1

Explanation:

let mass of body be m

let its constant acceleration be a

time-t

velocity -v

now its velocity at time t is v=at

force on the body is F=ma

power delivered is P=Fv

P=ma(at)

P=ma²t

therefore P is proportional to a² and t

Answer 2

Answer:-

We know that:-

→ Body mass = m

→ Acceleration = a

According to the Newton’s second law of motion:-

F = ma (constant)

We know that,

a = $\frac{dv}{dt}$ = constant

dv = dt x constant

On integrating,

$v = \alpha t \rightarrow \: 1$

Where, $\alpha$ is also a constant.

$v ∝ t \rightarrow \: 2$

The relation of power is given by:-

$\sf{\boxed{\boxed{P = F.v}}}$

From the equation 1 & 2,

$\to{\sf{\boxed{\boxed{P \propto t}}}}$

Thus, from the above we conclude that power is proportional to time.