If the velocity of a body is doubled its kinetic energy

To solve this problem, we need to understand the relationship between velocity and kinetic energy.

Step 1: Recall the formula for kinetic energy: KE = (1/2)mv^2, where KE is the kinetic energy, m is the mass of the body, and v is the velocity of the body.

Step 2: Let's assume the initial velocity of the body is v1 and the initial kinetic energy is KE1.

Step 3: According to the problem, the velocity of the body is doubled. So, the new velocity becomes 2v1.

Step 4: Now, we need to find the new kinetic energy, KE2, with the doubled velocity.

Step 5: Substitute the new velocity (2v1) into the kinetic energy formula: KE2 = (1/2)m(2v1)^2.

Step 6: Simplify the equation: KE2 = (1/2)m(4v1^2) = 2mv1^2.

Step 7: Compare the new kinetic energy (KE2) with the initial kinetic energy (KE1).

Step 8: According to the problem, the velocity is doubled, which means v1 is multiplied by 2.

Step 9: Substitute the value of v1 into the equation: KE2 = 2m(2v1^2) = 4mv1^2.

Step 10: Since the initial kinetic energy is KE1, we can write the equation as: KE2 = 4KE1.

Step 11: Therefore, if the velocity of a body is doubled, its kinetic energy becomes four times the initial kinetic energy.