Based on unit considerations alone, show that the power needed to accelerate a car of mass m (in kg) from rest to velocity V (in m/s) in time interval t (in s) is proportional to mass and the square of the velocity of the car and inversely proportional to the time interval.
Mass of the car = m (in kg)
Initial velocity = 0 (in m/s)
Final velocity = v (in m/s)
Time interval = t (in s)
Taking Left hand side
Power is defined as the rate of doing work or the amount of energy consumed in a second.
We know that work done = force x distance
W = F x d
Force = mass x acceleration
F = ma
Therefore the power can be written as