Question

A body is moved along a straight line by a machine delivering constant power. The distance travelled by the body in time $t$ is proportional to

• A. $t^{1/2}$
• B. $t$
• C. $t^{3/2}$
• D. $t^2$

Answer 1

Answer: (C)

$t^{3/2}$

Power is rate of doing work,

$P=\frac{W}{t}=\frac{F.s}{t}=F.v$$=\left(ma\right).\left(at\right)=m{a}^{2}t$

$⟹a^{2}t=\frac{P}{m}=constant$

Also $s=\frac{1}{2}a{t}^2$

$⟹s^2=\frac{1}{4}{a}^2{t}^4=constant.t^3$

$⟹s\propto t^{3/2}$