Question

Calculate the power generated by tention in a string in 1st 2 seconds of motion. Provided mass of body is 10kg and acceleration of body is g/2 in upward direction

Answer 1

here we see body moves upward direction hence, non-inertial frame
so, use concept of pseudo force .

now F is force acting on object

F =m(g+ a)
where a =g/2 upward acceleration
F = 10( g +g/2) = 15g
if g = 10m/s²

then ,
F = 150 N
instanteous velocity (v)= u + at = 0 + gt/2
=5t
total distance covered within 0≤ t≤ 2
s = ut + 1/2gt²= 1/2g/2t² =5/2t²= (2.5)t²

now,
total energy = kinetic energy + potential energy
1/2×10(5t)² + 10×10(2.5)t²
= 250t² + 125t²
=375t²

now ,
average power = total energy /total times
=375t²/t = 375t

now put t = 2
Power = 375×2 =750w

Answer 2

       Here it appears that there is a string pulling a body upward direction with a constant acceleration a = g/2. The body has mass m = 10 kg and starts from rest.

    The tension force T in the string is the one which pulls the body upwards against the gravity force W = mg.  Let g =10m/s²

     Perhaps the string goes over a pulley with a person pulling it or a heavier weight is hung from it.

T - m g = m a 
T = m (g+a) = 3 mg/2 = 3 * 10 * 10/2 = 150 N

Instantaneous velocity of m at t = v = u +at = g t /2 = 5 t   m/s
Instantaneous power causing KE of the body = P(t)
           P(t) = Force * velocity = 150 * 5 t 
                  = 750 t   Watts
However there is Power spent in raising the PE of the body too.

Height h gained by the body = ut+1/2 a t²
            h = 1/2 g/2  t² = 2.5 t²  meters 

Total energy of the body at time t = m g h + 1/2 m v²
    E(t) = 10 *10* 2.5 t² + 1/2 * 10 * (5t)²
           =  375 t²   Watts

Average power during 2 seconds
         = Total energy / time duration  = 1/t  * Integral P(t) dt  from t=0 to t
         = 375 t² / t
         = 375 t
         = 750 Watts   for t = 2 sec.