Ye cannae change the laws o

—–Original Message—–
From: [Some Guy]
To: Customer Service

[Part of your course] is in error in stating that double velocity is quadruple kinetic energy. Also in error stating that kinetic energy and stoping distance are directly related. Double velocity is double kinetic energy. Double velocity means double stopping time over which quadruple stopping distance will occur. Please use correct science when teaching Physics. Thanks and I hope that this mistake is not repeated on your exams.

—–Reply—–
From: Me
To: ["Letters You Don't Send to Customers" Department]

Your assertion that doubling velocity will also double kinetic energy is incorrect (using metric, since it’s easier):

Using the formula,
Kinetic energy = (1/2) * mass * velocity²

A person, assumed to be about 80kg, travelling at 40mph (17.8816 meters/sec):
(1/2) * 80 * 17.8816² = 12,790 joules
Doubling the velocity:
(1/2) * 80 * 35.7632² = 51,160 joules (12,790 * 4)

Or, four times the kinetic energy, measured in joules. You are, however, correct in stating that doubling velocity would translate to four times the stopping distance, but fail to mention why. We mean they are “directly related” in that an increase in velocity will directly lead to an increase in stopping distance. To round out your understanding of this topic, stopping distance is directly proportional to the square of the starting velocity:

Where x is the stopping distance, and assuming a friction coefficient of 0.8 (new tires, new tread), and gravitational constant of 9.8m/s:

distance = -17.8816²/2 * 0.8 * 9.8 = 1.8945m
distance = -35.7632²/2 * 0.8 * 9.8 = 7.5780m (1.8945 * 4)

Please don’t try and prove how smart you are to us; we’re not impressed, and incidentally, not changing our course content.