#### 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

1) `t^(1/2)`

2) t

3)`t^(3/2)`

4)`t^2`

#### Solution

2) t

Mass of the body = *m*

Acceleration of the body = *a*

Using Newton’s second law of motion, the force experienced by the body is given by the equation:

F =ma

Both *m* and *a *are constants. Hence, force *F *will also be a constant.

*F* = *ma* = Constant … (*i*)

For velocity *v*, acceleration is given as,

`a = (dv)/(dt)` = Constant

dv = Constant x dt

va = `alphat` ....(ii)

Where `alpha` is another constant

`v prop t`

Power is given by the relation:

*P = F*.*v*

Using equations (*i*) and (*iii*), we have:

*P *∝* t*

Hence, power is directly proportional to time.

Is there an error in this question or solution?

Solution 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 Concept: The Conservation of Mechanical Energy.