Question

6. A particle of mass 1 kg moves in a circular path of radius 1 m such that its speed varies with time as per equation \( v=3 t^{2} m / s \) where time \( t \) is in seconds. The power delivered by the force acting on the particle at \( t=1 s \), is: (1) 36 W (2) 20 W (3) 18 W (4) zero

Answer 1

Given,

v = 3t² ms^-1

Power is the work done using force in unit time.

P = \(\frac{F\times d}{t}\)

= F × v

= m × a × v

Now,

\(a = \frac{dv}{dt}\)

\(= \frac{d\ 3t^2}{dt}\)

= 6t m s^-2

Therefore,

P = 1 × 6t × 3t²

At t = 1s, the power is

P = 18 W