Ap Physics 1 Summer Assignment Worksheet (Page 11 of 13) in pdf

You will notice that only the linear function is a straight line. We can easily find the slope of our line by

measuring the rise and dividing it by the run of the graph or calculating it using two points. The value of the

slope should equal the constant k from the equation.

Finding k is a bit more challenging in the last three graphs because the slope isn’t constant. This should make

sense since your graphs aren’t linear. So how do we calculate our constant, k? We need to transform the non-

linear graph into a linear graph in order to calculate a constant slope. We can accomplish this by transforming

one or both of the axes for the graph. The hardest part is figuring out which axes to change and how to change

them. The easiest way to accomplish this task is to solve your equation for the constant. Note in the examples

from the last page there is only one constant, but this process could be done for other equations with multiple

constants. Instead of solving for a single constant, put all of the constants on one side of the equation. When you

solve for the constant, the other side of the equation should be in fraction form. This fraction gives the rise and

run of the linear graph. Whatever is in the numerator is the vertical axis and the denominator is the horizontal

axis. If the equation is not in fraction form, you will need to inverse one or more of the variables to make a

fraction. First let’s solve each equation to figure out what we should graph. Then look below at the example and

complete the last one, a sample AP question, on your own.

State what should be graphed in order to produce a linear graph to solve for k.

Inverse Graph

Vertical Axis:_____________________

Horizontal Axis: ____________________

Inverse Square Graph Vertical Axis:_____________________

Horizontal Axis: ____________________

Power (Square) Graph Vertical Axis:_____________________

Horizontal Axis: ____________________

Chemistry Example

Let’s look at an equation you should remember from chemistry. According to Boyle’s the law, an ideal gas

obeys the following equation ��

��

= ��

��

= ��. This states that pressure and volume are inversely related, and

the graph on the left shows an inverse shape. Although the equation is equal to a constant, the variables are not

in fraction form. One of the variables, pressure in this case, is inverted. This means every pressure data point is

divided into one to get the inverse. The graph on the left shows the linear relationship between volume V and

the inverse of pressure 1/P. We could now calculate the slope of this linear graph.

Ap Physics 1 Summer Assignment Worksheet Page 11