Question

An object is moving with velocity V. The velocity of the moving object is doubled. Identify which of the following statements about the moving object is correct?
A. The kinetic energy of the moving object increases by three.
B. The displacement of the object increases by three.
C. The momentum of the object increases by three.
D. The frictional force increases by three.
E. None of these quantities increase by three.

Answer 1

Define each term in the option and give their relation to the velocity of the moving object. Find the type of relation between the terms in the option and the velocity. Kinetic energy is the energy possessed by a moving object. Velocity is the rate of change of displacement.

Complete step by step answer:
1. Kinetic energy:

If V is the velocity of the moving object then its kinetic energy is given as

$K.E.=\dfrac{1}{2}m{{v}^{2}}$
$\therefore K.E.\propto {{v}^{2}}$

Therefore, the kinetic energy of a moving object is proportional to the square of its velocity.
Thus, if velocity is doubled then kinetic energy will become four times.
Therefore, the kinetic energy of the moving object increases by three times its initial value.

2. Displacement:

The velocity of an object is defined as the displacement covered by an object in a given interval of time.
Therefore, velocity in terms of displacement is given as

$\text{Velocity=}\dfrac{\text{Displacement}}{\text{Time interval}}$

From the above expression we can say that in a given time interval, the displacement covered by an object is directly proportional to its velocity.

Thus, $velocity\propto displacement$
Hence, if velocity is doubled then the displacement of the object will also be doubled.

3. Momentum:

The momentum of an object is given as
$P=mv$
Thus, from the above equation, it can be seen that the momentum of an object is directly proportional to its velocity. Hence if the velocity is doubled the momentum of the body will also be doubled.

4. Frictional force:

The frictional force acting on a moving object is not related to the velocity of the moving object, rather than it is related to its acceleration.
Thus, from the above discussion, we can conclude that only option A is correct.

Note:
Note that some terms depend on the change in velocity rather than the only velocity. For example, acceleration: rate of change of velocity. Few quantities are not directly related to the velocity, just as the frictional force. Velocity is a vector quantity, so it has both direction and magnitude. It also observed that many quantities depend only on the magnitude of velocity whereas others depend on both magnitude and direction of velocity.