A Robin
B Alia
C Sara
D All have same power
\(P_{avg}\; = \dfrac{W}{\Delta\;t}\)
W = f (t)
As \(P\;=\;\dfrac{dW}{dt}\)
\(P = \dfrac{d}{dt}\;[f(t)]\)
A 12 W
B 10 W
C 14 W
D 16 W
\(F = m × \dfrac{d^2x(t)}{dt^2}\)
Power P = F.v
\(P = \dfrac{md^2x(t)}{dt^2}\;× \;\dfrac{dx(t)}{dt}\)
\(W = \;\Delta \;KE\)
\(W = (K_f-K_i)\)
\(P_{avg} = \dfrac{W}{\Delta t}\)
\(P_{avg} = \dfrac{K_f - K_i}{\Delta t}\)
where K_{f} = Final kinetic energy
K_{i} = Initial kinetic energy
\(\Delta\,t\) = Time interval
Power at given instant of time is known as instantaneous power.
Instantaneous power is the limiting value of the average power as
\(\Delta t \) → 0
\(P=\lim\limits_{\Delta t\rightarrow0}\; \dfrac{W}{\Delta t\;}\;\;=\;\;\dfrac{dW}{dt}\)
\(dW = \vec{F}.\;{d\vec s}\)
\(\dfrac{dW}{dt}\; =\;\vec{F}.\;\dfrac{d\vec{s}}{dt}\)
\(\dfrac{dW}{dt}\;=\;\vec{F}. \vec{v}\)
\(P\; = \vec{F}.\vec{v}\)