Question

Consider the exponent ^2 in the Kinetic Energy formula KE = (0.5mv)(v^2). If you go twice as fast, your kinetic energy becomes:

a) Four times as much
b) Half as much
c) Twice as much
d) The same

Answer 1

The kinetic energy is proportional to the square of the velocity, so if the velocity doubles, the kinetic energy quadruples, making the answer a) Four times as much.

Step-by-step explanation:

The kinetic energy (KE) formula is given by KE = 0.5mv2, where m is the mass and v is the velocity of the object. Since kinetic energy is proportional to the square of the velocity, if you go twice as fast, your velocity is squared, resulting in kinetic energy that is four times as much. Therefore, accelerating an object to double its original velocity will result in quadrupling its kinetic energy.

For example, if a car is traveling at 20 mph and accelerates to 40 mph, its velocity has doubled. Following the kinetic energy formula (KE = 0.5mv2), if the initial kinetic energy at 20 mph is KE1, then at 40 mph, the kinetic energy KE2 would be:

• KE1 = 0.5 * m * (20 mph)2
• KE2 = 0.5 * m * (40 mph)2 = 0.5 * m * 4 * (20 mph)2 = 4 * KE1

Therefore, the correct answer to the question is option a) Four times as much.