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**

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