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5.Work, Energy, Power and Collision
normal
When a constant force is applied to a body moving with constant acceleration, power does not remain constant. For power to be constant, the force has to vary with speed as follows
A
$F \propto \frac{1}{\upsilon }$
B
$F \propto \frac{1}{\sqrt \upsilon }$
C
$F \propto {\upsilon }$
D
$F \propto {\upsilon ^2}$
Solution
As $a=\frac{d v}{d t}=\frac{F}{m}=$ constant, hence, on integration,
we get $;$
$\mathrm{v}=\frac{\mathrm{F}}{\mathrm{m}} \mathrm{t}$
So, power, $P=\mathrm{F} \mathrm{v}=\frac{\mathrm{F}^{2}}{\mathrm{m}} \mathrm{t}$
i.e., $p$ $\infty$ $t$ For power to be constant, $\mathbf{Fv} =$ constant, i.e.,
$\mathrm{F} \propto \frac{1}{\mathrm{v}}$
Standard 11
Physics
