Question

A machine is delivering constant power to drive a body along a straight line. What is the relation between the distance travelled (S) by the body against time (t)?

• A. $s^2\alpha t^3$
• B. $s^2\alpha t^{-3}$
• C. $s^2\alpha t^2$
• D. $s\alpha t^3$

Answer 1

The correct option is A $s^2\alpha t^3$

$Power=Force\left(F\right)\ast Velcoity\left(V\right)$

$F=Mass\left(m\right)\ast Acc\left(a\right).$

$a=\frac{Distance\left(S\right)}{Time(t{)}^2}$

$V=\frac{Distance\left(S\right)}{Time\left(t\right)}$

Put Values of F and V in Power we get,
$Power=m\ast \frac{S}{t^2}\ast \frac{S}{t}$
Since Power and mass are constant therfore
$S^2\alpha t^3$