Question

A body of mass m is accelerated uniformly from rest to speed v in a time T . The instantaneous power delivered to the body as a function of time , is given by [AIEEE 2005 , 04]

(a)mv² /T²*t
(b) mv²/T²*t²
(c) 1/2mv²/T²*t
(d) 1/2mv²/T²*t² ​

Answer 1

Explanation:

at time t

power is work /time

=F×S/t

=m×V/T×1/2 ×a ×t

=mV/2T ×V/T ×t

=mV²/2T² ×t

Mark as brainliest

Answer 2

${\sf\large{\underline{\underline{ Solution:-}}}}$

GivEn:

• Mass (m) = m
• Speed (s) = v
• Time (t) = t

To Find:

• The instantaneous power delivered to the body as a function of time?

Solution:

From the 1st Motion of Equation,

we get;

$\\ \hookrightarrow{\boxed{\sf\purple{ v = u + at}}} \\ \\ \hookrightarrow{\sf{ v = 0 + at}} \\ \\ \hookrightarrow{\bf\large{a = \dfrac{v}{t} }}$

Now,

We have to find force!

$\\ \bullet{\boxed{\sf\large\orange{ F = ma}}} \\ \\ \hookrightarrow{\bf\large{ ma = \dfrac{mv}{t} }}$

$\\ {\sf{ Velocity \ acquired \ in \ t \ sec = at = \dfrac{v}{t} t}}$

Then We can find power;

we have;

$\\ {\sf\large{ F \times v} } \\ \\ \hookrightarrow{\bf\large{ \dfrac{mv}{t} \times \dfrac{vt}{t} }} \\ \\ \hookrightarrow{\boxed{\bf\large\green{ \dfrac{mv^2t}{t^2} }}}$