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

• A. t^1/2
• B. t
• C. t^3/2
• D. t²

Answer 1

The correct option is B

t

Step1: Given data

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration.

Step2: Formula used

$P=Fv[whereP=power,F=force,v=velocity]$

Step3: Solution

Using the first equation of motion

$v=u+at[wherev=finalvelocity,u=initialvelocity,a=acceleration,t=time]$

It is given to us that the body is initially at rest which means the initial velocity is zero (the body is not moving at all). $u=0$

$$\begin{gathered} v=0+at \\ v=at \end{gathered}$$

We know that the force is the product of mass and acceleration $F=ma$

Therefore power becomes,

$$\begin{gathered} P=Fv \\ P=ma\times at \\ P=m{a}^{2}t \end{gathered}$$

Here, mass and acceleration both are constant. Therefore power is directly proportional to time.

$P\propto t$

Hence, option B is the correct answer.