Question

A body of mass $2kg$ is driven by an engine delivering a constant power of $1J{s}^{-1}$. The body starts from rest and moves in a straight line. After $9s$ the body has moved a distance (in $m$) _____________.

Answer 1

Step 1. Given data

Mass of the body, $m=2kg$

Power of the engine, $P=1J{s}^{-1}$

Time, $t=9s$

Step 2. Finding the final velocity, $v$

We know that,

$Power=Work\times time$

$1=Work\times 9$

$Work=\frac{1}{9}J$ [$eq\left(1\right)$]

From the Work-Energy theorem,

$Work=changeinkineticenergy$

$Work=\frac{1}{2}m\left(v^2-u^2\right)$ [$v$ is the velocity, initial velocity, $u=0$]

From $eq\left(1\right)$, we get

$\frac{1}{9}=\frac{1}{2}\times 2\times v^2$

$v=3m{s}^{-1}$

Step 3. Finding the distance moved by the body, $x$

Also, the Velocity is the change in the position with respect to the time.

$v=\frac{dx}{dt}$

$dx=v.dt$

Now, integrating both the side

$x=\int v.dt$

$x={\int }_0^{9}3.dt$

$x=3{\left[t\right]}_0^9$

$x=3\times \left(9-0\right)$

$x=18m$

Therefore, the distance moved by the body is $18m$.