Question

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

• A. ${{t}^{1/2}}$
• B. ${{t}^{3/2}}$
• C. ${{t}^{2}}$
• D. ${{t}^{3/4}}$

Answer 1

Answer: (B)

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

Answer 2

As power $=F\times \upsilon =m\frac{dv}{dt}\times v=$ constant k $\upsilon d\upsilon =\frac{k}{m}dt$ ?(i) Now integrating equation (i), we get ${{\upsilon }^{2}}=\frac{2kt}{m}$ or $\upsilon =\frac{dx}{dt}=\sqrt{\frac{2k}{m}}{{t}^{1/2}}$ hence $x\propto {{t}^{3/2}}$