Question

The work W0 is required to accelerate a carfrom rest to the speed v0.

(a) How much work (in terms of W0) is required to accelerate the car from rest to the speed v0/2?
______W0
(b) How much work is required to accelerate the car fromv0/2 to v0? _______W0

Answer 1

Okay, here are the steps to solve this problem:

(a) To accelerate the car from rest to v0/2, the required work is proportional to the square of the final velocity.

So W = k*v^2 (where k is some constant)

Setting v = v0/2, the work required is:

W = k*(v0/2)^2 = k*v0^2 / 4

Therefore, the work required is W0/4

(b) To accelerate the car from v0/2 to v0, the required work is:

W = k*v^2 (where v starts at v0/2)

Setting v = v0, the work required is:

W = k*(v0/2)^2 * 2 = k*v0^2 / 2 = W0/2

Therefore,

(a) W0/4

(b) W0/2

Does this make sense? Let me know if you have any other questions!