Question

A vehicle is moving from rest to a velocity of u m/s. Let the energy required for this process be E. The energy required to accelerate the vehicle from velocity u to 2u is x times E. What is the value of x?

(a) 2
(b) 4
(c) 8
(d) 16

Answer 1

The energy required to accelerate a vehicle from velocity u to 2u is four times the energy required to accelerate it from rest to velocity u, hence the correct answer choice is (b) 4.

Step-by-step explanation:

The question relates to the kinetic energy of a vehicle as it accelerates from rest to a given velocity, and then from that velocity to double its speed.

According to the work-energy theorem in physics, the kinetic energy (KE) of an object is given by the equation KE = ½ m v², where m is the mass of the object and v is its velocity. Therefore, when the vehicle moves from rest (initial velocity, v = 0) to a velocity of u, the energy required (E) to do so is E = ½ m u².

When accelerating the vehicle from velocity u to 2u, the final kinetic energy is KE = ½ m (2u)² = 2² ½ m u² = 4E. Therefore, the energy required for this process is 4 times the initial energy E, which means x = 4.

The correct option answer in this final answer is (b) 4.