Question

The kinetic energy of an object of mass m in motion with velocity of $5m/s$ is $25J$. What will be its kinetic energy when its velocity is doubled?
a. $1000J$
b. $25J$
c. $100J$
d. $4J$

Answer 1

Hint: From the information which is given in the question, we can find the mass of the object , which we can later use to find the new kinetic energy.

Complete step by step answer:
Following information is given in the question
Velocity of object,$v = 5m/s$
Kinetic energy of object, $K = 25J$

We know that,
$K = \dfrac{1}{2}m{v^2}$
Putting the values in equation, we get
$25 = \dfrac{1}{2}m{(5)^2}$
$m = 2kg$

Now it is given in the question that the velocity is doubled
So,
$
  {v_{new}} = 2v \\
  {v_{new}} = 2(5) \\
  {v_{new}} = 10m/s \\
 $

New kinetic energy will be
$
  {K_{new}} = \dfrac{1}{2}m{v_{new}}^2 \\
  {K_{new}} = \dfrac{1}{2} \times 2 \times {10^2} \\
  {K_{new}} = 100J \\
 $

c) is correct.

Additional information:
Kinetic energy of an object is the energy that it possesses due to its motion. It is also defined as the work needed to accelerate a body of mass m from rest to a particular velocity. Energy is a scalar quantity which means it does not depend on direction and is always positive. When we double the mass, we double the energy but when we double the velocity, kinetic energy increases by four times.

Note: In this question, the velocity is very small as compared to speed of light because we are in the domain of Newtonian mechanics. Newtonian mechanics deals with the motion of objects moving at speeds which are very small as compared to the speed of light. At smaller speeds we can consider mass to be constant but this is not true for higher speeds. At higher speeds which are comparable to the speed of light, Newtonian mechanics break down and give invalid results. This is because of the fact that mass increases with the increase in velocity. At smaller speeds, this change in mass is so less that we can neglect it but this change becomes significant when we are at the speeds comparable to the speed of light.