Kinetic Energy

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.