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 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
${t^{1/2}}$
${t^{3/4}}$
${t^{3/2}}$
${t^2}$
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
$P = Fv = mav = m\left( {\frac{{dv}}{{dt}}} \right)\;v$ $⇒$ $\frac{P}{m}dt = v\;dv$
$⇒$ $\frac{P}{m} \times t = \frac{{{v^2}}}{2}$ $⇒$ $v = {\left( {\frac{{2P}}{m}} \right)^{1/2}}{(t)^{1/2}}$
Now $s = \int_{}^{} {v\;dt = \int_{}^{} {{{\left( {\frac{{2P}}{m}} \right)}^{1/2}}{t^{1/2}}dt} } $
$s = {\left( {\frac{{2P}}{m}} \right)^{1/2}}\left[ {\frac{{2{t^{3/2}}}}{3}} \right]$ $⇒$ $s \propto {t^{3/2}}$
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