Question

A particle of mass M starting from rest undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is

Answer 1

Answer:

Power delivered in time T is

$P= \vec F . \vec V =MaV$

$or \ P=MV \dfrac {dv}{dt}$

$PdT=MVdV$

$PT= \dfrac {M{V}^{2}}{2}$

$P = \dfrac {M{V}^{2}}{2T}$

Answer 2

Dear student,

Given :-

• mass = m
• initial velocity = 0
• final velocity = v
• duration = t

To find :-

• the power delivered to the particle in time T.

Solution:-

Since the question talks about a particle travelling in time t, we talk power in terms of average power. Now, we know that, for average power that;

          P = Totol Work done/ time

or,       P = Wtotal/ time

or,       P = Δ K.E. / time

or,       P = Final K.E. - Initial K.E./ time

or,       P = 1/2 mv² - 0 / T

or,       P = mv²/ 2T

Hence, the power delivered to the particle is mv²/ 2T watt.