a body starts from rest and acquire avelosity V in time T. The instantaneous power developed to the body is proportionalto
To find the expression for the instantaneous power developed on a body that starts from rest and acquires velocity V in time T, we need to understand the concept of power.
Power is defined as the rate at which work is done or energy is transferred. In the case of a moving body, the power developed can be calculated as the product of force and velocity.
Since the body starts from rest, it must have undergone an acceleration to acquire velocity V in time T. According to Newton's second law of motion, the net force acting on an object is equal to its mass multiplied by the acceleration it experiences.
So, let's consider the mass of the body as m, and the acceleration it undergoes as a.
Now, we know that acceleration is the change in velocity divided by the change in time. In this case, the change in velocity is V (final velocity) because the body starts from rest, and the change in time is T.
So, we can write the expression for acceleration as:
a = V / T
Now, according to Newton's second law, the net force acting on the body is given by:
F = m * a
Substituting the expression for acceleration, we get:
F = m * (V / T)
Finally, the instantaneous power developed is the product of force and velocity, so:
Power = F * V
Substituting the expression for force, we get:
Power = (m * (V / T)) * V
Simplifying further:
Power = m * (V^2 / T)
Thus, the instantaneous power developed on the body is proportional to the square of velocity V and inversely proportional to the time T.