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# Based on unit considerations alone, show that the power ISBN: 9780071284219 39

## Solution for problem 35P Chapter 1

Fluid Mechanics | 2nd Edition

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Problem 35P

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-by-Step Solution:

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 = Step 4 of 6

Step 5 of 6

##### ISBN: 9780071284219

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