If the percentage error in velocity is 100%, meaning the velocity is doubled or multiplied by a factor of 2, we can calculate the resulting error in kinetic energy.
The kinetic energy of an object is given by the formula:
KE = (1/2) * m * v^2
Where: KE is the kinetic energy m is the mass of the object v is the velocity of the object
Let's assume the original velocity is v, and the new velocity with a 100% error is 2v.
The original kinetic energy (KE1) is given by:
KE1 = (1/2) * m * v^2
The new kinetic energy (KE2) with the 100% error is given by:
KE2 = (1/2) * m * (2v)^2 = (1/2) * m * 4v^2 = 2 * (1/2) * m * v^2 = 2 * KE1
To calculate the error in kinetic energy, we subtract the original kinetic energy from the new kinetic energy:
Error in KE = KE2 - KE1 = 2 * KE1 - KE1 = KE1
Therefore, the error in kinetic energy with a 100% error in velocity is equal to the original kinetic energy.