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.

Step 1:

Mass of the car = m (in kg)

Initial velocity = 0 (in m/s)

Final velocity = v (in m/s)

Time interval = t (in s)

Step 2:

To prove

Power

Step 3:

Taking Left hand side

Power is defined as the rate of doing work or the amount of energy consumed in a second.

P =

We know that work done = force x distance

W = F x d

P =

Force = mass x acceleration

F = ma

Therefore the power can be written as

P =