Question

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

• A. $t$
• B. ${{t}^{1/2}}$
• C. ${{t}^{5/2}}$
• D. ${{t}^{3/2}}$

Answer 1

Answer: (D)

${{t}^{3/2}}$

Answer 2

: Power P = (force F) $\times$ (velocity v) $P=m\times$ acceleration $\times v$ or $P=ma\times (at)\Rightarrow {{a}^{2}}=\frac{p}{m\times t}$ Now $S=\frac{1}{2}a{{t}^{2}}$ $=\frac{1}{2}\times \sqrt{\frac{P}{mt}}.{{t}^{2}}=\frac{1}{2}\times \sqrt{\frac{P}{m}}.{{t}^{3/2}}$ S = (constant) $\times {{t}^{3/2}}$ or Distance $(S)\propto {{t}^{3/2}}$