MCQ
A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :
- A$t^2$
- B$t^{2 / 3}$
- C$t^{3 / 2}$
- Dt
✓
Answer
$ P =\text { costant } \Rightarrow FV =\text { constant }$
$\Rightarrow m \frac{ dV }{ dt } V =\text { constant }$
$\int_0^{ V } VdV =( C ) \int_0^{ t } dt$
$\left(\frac{ V ^2}{2}\right)= Ct$
$V \propto t ^{1 / 2}$
$\frac{ ds }{ dt } \propto t ^{1 / 2}$
$\frac{s}{ s } ds = K \int_0^{ t } t ^{1 / 2} dt$
$0$
$S= K \times \frac{2}{3} t ^{3 / 2}$
$S \propto t ^{3 / 2}$
$\therefore$ displacement is proportional to $( t )^{3 / 2}$
$\Rightarrow m \frac{ dV }{ dt } V =\text { constant }$
$\int_0^{ V } VdV =( C ) \int_0^{ t } dt$
$\left(\frac{ V ^2}{2}\right)= Ct$
$V \propto t ^{1 / 2}$
$\frac{ ds }{ dt } \propto t ^{1 / 2}$
$\frac{s}{ s } ds = K \int_0^{ t } t ^{1 / 2} dt$
$0$
$S= K \times \frac{2}{3} t ^{3 / 2}$
$S \propto t ^{3 / 2}$
$\therefore$ displacement is proportional to $( t )^{3 / 2}$
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