Concept: Kinetic energy (KE) is the energy an object possesses due to its motion. It depends on the object's mass and its velocity. Step 1: Recall the Formula for Kinetic Energy
The kinetic energy of an object is given by the formula:
where:
is the mass of the object (assumed to be constant in this problem).
is the velocity (or speed, since KE is a scalar) of the object. Step 2: Define Initial and Final States
Let the initial velocity of the object be .
The initial kinetic energy ( ) is:
The problem states that the velocity of the object becomes double. So, the new (final) velocity, let's call it , is:
Step 3: Calculate the New Kinetic Energy
Now, we calculate the new kinetic energy ( ) using the new velocity :
Substitute the expression for ( ) into this equation:
Step 4: Simplify the Expression for New Kinetic Energy
When we square , both the and are squared:
Now substitute this back into the equation for :
We can rearrange the terms to make the comparison clearer:
Step 5: Compare the New Kinetic Energy with the Initial Kinetic Energy
Notice that the term in the parentheses, , is exactly the expression for the initial kinetic energy, .
So, we can write:
This shows that the new kinetic energy is four times the initial kinetic energy. Therefore, if the velocity of an object becomes double, its kinetic energy will be four times.