physics course before and have never had a calculus course before but are currently enrolled in a
calculus course. If you have already taken calculus, physics, or both, then you have a well-
earned advantage.)
Two points of emphasis regarding the mathematical component of your solutions to physics
problems that have a mathematical component are in order:
(1) You are required to present a clear and complete analytical solution to each problem. This
means that you will be manipulating symbols (letters) rather than numbers.
(2) For any physical quantity, you are required to use the symbol which is conventionally used
by physicists, and/or a symbol chosen to add clarity to your solution. In other words, it is
not okay to use the symbol x to represent every unknown.
Aside from the calculus, here are some of the kinds of mathematical problems you have to be
able to solve:
Problems Involving Percent Change
A cart is traveling along a track. As it passes through a photogate1 its speed is measured to be
3.40 m/s. Later, at a second photogate, the speed of the cart is measured to be 3.52 m/s. Find the
percent change in the speed of the cart.
The percent change in anything is the change divided by the original, all times 100%. (I’ve
emphasized the word “original” because the most common mistake in these kinds of
problems is dividing the change by the wrong thing.)
The change in a quantity is the new value minus the original value. (The most common
mistake here is reversing the order. If you forget which way it goes, think of a simple
problem for which you know the answer and see how you must arrange the new and
original values to make it come out right. For instance, suppose you gained 2 kg over the
summer. You know that the change in your mass is +2 kg. You can calculate the
difference both ways—we’re talking trial and error with at most two trials. You’ll quickly
find out that it is “the new value minus the original value” a.k.a. “final minus initial” that
yields the correct value for the change.)
Okay, now let’s solve the given problem
change
% Change =
100 %
(1-1)
original
Recalling that the change is the new value minus the original value we have
1 A photogate is a device that produces a beam of light, senses whether the beam is blocked, and typically sends a
signal to a computer indicating whether the beam is blocked or not. When a cart passes through a photogate, it
temporarily blocks the beam. The computer can measure the amount of time that the beam is blocked and use that
and the known length of the cart to determine the speed of the cart as it passes through the photogate.
3