The Three Column Method (A.k.a the GPSM)

This is the method you must use to solve problems in AP, Pre-AP and Conceptual Physics. You will also find this method useful in all classes wherein you are confronted with word problems.

Divide your paper into three columns. (Depending on your computer you may or may not see the following in a three-column format. So, the first column has the information from the problem, the middle column has the equations, and the third column has the math work.)

In this first column put the information from the problem:

· The quantities, such as velocity, time, distance, force, etc

• The amount of the quantity, for example 24, or 5
• The unit for the quantity such as m/s, s, m, N, etc

· The unknown with a question mark for the number and the proper SI units

In this middle column put the equations that will be used to solve the problem.

• Start with the basic equation.
• When necessary, solve the basic equation for the unknown in this column.
• If more than one equation is necessary put the equations here as well, starting with the basic form of that equation.
• If necessary solve this equation for the unknown quantity.

In this third column do all of the math work using the equations from the middle column.

• Do the math work with the numbers.
• Do the math work with the units as well.
• Check the units of your final solution with the units of the of the unknown in the first column. If they do not agree check your equations in the middle column.
• Put your final solution in a box.

Here is an example:

A car accelerates uniformly in a straight line from rest at the rate of 2.7m/s². (a) How fast will the car be going after it has traveled 0.62km? (b) How long will it take this car to travel 0.062km?

(N.B. Your computer may not have the necessary program to open the equation program I used to solve this problem. If this happens to you see Mr. Young or try another computer.)

v_i = 0 m/s v_f² = v_i² + 2ad v_f = (sq rt) 2(2.7 m/s² x 62 m)

a = 2.7 m/s² a = v_f – v_i / t v_f = (sq rt) 2(167.4 m²/s²)

d = 0.062km t = v_f – v_i / a v_f = (sq rt) 334.8 m²/s²

v_f = ? m/s v_f = 18.3 m/s

t = ? s

t = 18.3 m/s – 0 m/s / 2.7 m/s²

t = 6.8 s