Question

A body is moving along a straight line delivering power given as P = at, then work (W) done is given for time 0 to t is

• A. W = a
• B. W = $\frac{1}{2}a{t}^2$
• C. W = $2a{t}^2$
• D. W = $a^2{t}^2$

Answer 1

The correct option is B W = $\frac{1}{2}a{t}^2$

Given that ,

Power , $P=at$

We know that

$P=\frac{dW}{dt}$

$⟹\frac{dW}{dt}=at$

$⟹dW=atdt$

$⟹W={\int }_0^{t}atdt$

$⟹W=\frac{1}{2}a{t}^2$

$\therefore$ Work done for time 0 to t , $W=\frac{1}{2}a{t}^2$