Question

A body is initially at rest . It undergoes one dimensional motion with constant acceleration . How is the power ( P ) related to time ( T ) ?​

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption

Mass of the body

= m

Acceleration of the body

= a

${\boxed{\sf\:{According\;to\;newton\;2^{nd}\;law\;of\;Motion}}}$

Force = Mass × Acceleration

Here we have

◆Mass and acceleration is constant.

◆Force will be also constant

Force = mass × acceleration (which is constant)

${\boxed{\sf\:{Situation\;- Uniform\;linear\;motion}}}$

v = u + at

v = (0) + at

v = at

Power = Force × velocity (P = fv)

◆We have v = at

$\fbox{Hence,}$

Power = mass × a × at

Power = ma² × t

◆Acceleration = Constant

So,

◆Power is directly proportional to time (P∝t)

Answer 2

Answer:

$\boxed{\red {given \: that }}\: \\ \\ body \: is \: at \: rest \: \\ with \: a \: constant \: acceleration \\ \\ \\ we \: know\: that \\ \\ \green{by \: second \: law \: of \:motion \: } \\ \\ \implies \: force = \: m \: a \: \\ \\ now \: from \: equation \: of \: motion \\ \\ \implies \red{v = u \: + at} \\ \\ \\ we \: know \: that \\ \\ \implies \: \pink{p = f \times v} \\ \\ \implies \: p = ma(u + at) \\ \\ because \: it \: at \: rest \: so \: initial \: \\ velocity(u) = 0 \\ \\ now \: \\ \\ \implies \: p = m {a}^{2} t \\ \\ \\ here \: mass \: and \: acceleration \: is \: \\ constant \\ \\ we \: can \: say \: that \: \\ power \: is \: directly \: proportional \: to \\ time$