A body of mass m, accelerates uniformly from rest to v1 in time t1. The instantaneous power delivered to the body as a function of time t is

We need to determine the instantaneous power delivered to a body of mass m, which accelerates uniformly from rest to velocity v1 in time t1.

Step 1: Find the acceleration
Since the motion is uniformly accelerated, we use the equation of motion:

v = u + at

Given that initial velocity u = 0 and final velocity is v1 at time t1, we get:

v1 = 0 + a * t1
=> a = v1 / t1

So, the velocity at any time t during this motion is:

v = a * t = (v1 / t1) * t

Step 2: Find Instantaneous Power
Instantaneous power is given by:

P = F * v

Since force F is given by Newton’s second law:

F = m * a

Substituting a = v1 / t1, we get:

F = m * (v1 / t1)

Now, substituting the velocity expression v = (v1 / t1) * t into P = F * v:

P = [m * (v1 / t1)] * [(v1 / t1) * t]

=> P = m * (v1^2 / t1^2) * t

Final Answer:
The instantaneous power delivered to the body as a function of time t is:

P(t) = (m * v1^2 / t1^2) * t