Slope
Also called Gradient, Rise over run
Slope is how much the vertical quantity on a graph changes per unit change in the horizontal quantity, found as rise divided by run. On a physics graph it carries units, and those units identify which physical quantity the slope represents.
Slope and area are the two operations AP asks you to perform on graphs, and they answer opposite questions. Slope gives you a rate of change; area gives you an accumulated total.
The AP Physics 1 essential knowledge statements that hand a slope a name all follow one pattern, the derivative of the vertical quantity:
- Instantaneous velocity is the slope of a position-time graph (EK 1.3.A.4.i).
- Instantaneous acceleration is the slope of a velocity-time graph (EK 1.3.A.4.ii).
- The net external force on a system is the slope of a momentum-time graph (EK 4.2.A.5).
- The net torque on an object is the slope of an angular-momentum-time graph (EK 6.3.C.3).
Curved graphs need a tangent. Rise over run between two distant points gives an average over that interval. For a value at an instant, take the slope of the tangent line, which is what each statement above specifies. AP Physics C writes the same operation as a derivative.
Units name the quantity. Divide the vertical axis unit by the horizontal one. Metres over seconds is a velocity; newton seconds over seconds is a force. A slope in units nothing in the problem uses means you plotted the wrong pair.
In the Experimental Design and Analysis question the slope is usually a combination of constants rather than the constant you want, so say what it equals in symbols before solving. Linearization is what makes the plot straight, and the slope is read off the best fit line, never off two raw data points.