Question

The engine of a car does work W to increase the velocity of the car from 0 to v. What is the work done by the engine to increase the velocity of the car from v to 2v. A. W. B.2w C. 3w D. 4w

Answer 1

Work done = Force * distance

Force = mass * acceleration
Assuming Constant acceleration = a
Let mass of car = m

Force = ma

We know,
V^2 = u^2 + 2as
where,
V is final Velocity
U is Initial Velocity

s = (v^2 - u^2) / 2a

Work done in case of 0 to V = ma * s
W = ma*(v^2 - u^2) / 2a
W = mv^2/2 ------------1

Work done in case of v to 2V = ma * s
w2 = ma * (v^2 - u^2) / 2a
w2 = m*((2v)^2 - (v)^2) /2
w2 = m * (4v^2 - v^2) /2
w2 = 3 * mv^2/2

Substituting Value from Eq 1

W2 = 3 * W

Work done by the engine to increase the velocity of the car from v to 2v = 3W