Question

A body of mass 1 kg begins to move under the
action of a time dependent force F = (2tî + 3t2jN,
where i and į are unit vectors along x and y
axis. What power will be developed by the force at
the time t?
[NEET-2016]
(1) (2+3 + 315) W (2) (2t2 + 342) W
(3) (2+2 + 414) W (4) (2+3 + 34) W​

Answer 1

Answer:

(1)

Explanation:

instantaneous power=force . velocity

=f(x)*v(x)+f(y)*v(y)

And, F=ma

and as m=1kg so F=a

so, we split the acceleration in two coordinates:-

$\frac{dvx}{dt} = 2t$

$dvx = 2t.dt$

$vx = {t}^{2} \: \: \: \: ............(1)$

and now calculate vy at any time t.

$\frac{dvy}{dt} = 3 {t}^{2}$

$dvy = 3 {t}^{2} .dt$

$vy = {t}^{3} \: \: \: \: ............(2)$

from equation (1) and (2)

$v(t) = {t}^{2} i + {t}^{3} j$

power=f(x)*v(x)+f(y)*v(y)

$power = 2 {t}^{3} + 3 {t}^{5}$

HOPE THAT HELPS.

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