High School Physics : Understanding Independent and Dependent Variables
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Example Questions
Example Question #1 : Understanding Independent And Dependent Variables
A scientist measures how far a particle travels within a given amount of time. Every second she measures how far it has gone, and creates a graph of her results. What is the independent variable in this experiment?
Time
It will depend on the shape of the graph
Both variables are independent
Neither variable is independent
Distance
Time
An independent variable is manipulated by the experimenter. Any changes made are predictable. The dependent variable reacts to changes made to the independent variable. Its changes are not controlled by the experimenter and can be hard to predict.
In this particular experiment, the scientist is measuring how the particle's distance changes over a given time. She is able to control the amount of time that she measures, but is only able to observe the distance traveled.
In the graph, the independent variable will be graphed on the x-axis.
Example Question #2 : Understanding Independent And Dependent Variables
When looking at velocity in terms of distance and time, what is the independent variable?
Displacement
Time
Velocity
Distance
Acceleration
Time
There are a few ways to think of this question. The first is to imagine you are graphing velocity. Since the equation is 
The other way to think of this is to ask yourself what our "inputs" and "outputs" would be if we were measuring velocity. Imagine you're walking down the street and you record how far you travel every second. The time is what you are "inputting" and your distance travelled is your "output."
Example Question #2 : Understanding Independent And Dependent Variables
You are looking at a graph of the motion of a vehicle. On the y-axis is displacement and on the x-axis is time. Which of the following is the independent variable?
Time
Velocity
Acceleration
Displacement
Distance
Time
Independent variables are predetermined by the experimenter and can be manipulated to change the measured dependent variable. Independent variables are generally graphed on the x-axis, while dependent variables are generally graphed on the y-axis.
In this question, time is the independent variable and displacement is the dependent variable. The experimenter can select sampling times, but cannot necessarily predict the displacement that will be measured at each point. This defines time as the independent variable.
Example Question #1 : Understanding Independent And Dependent Variables
Where is the independent variable most commonly displayed on a graph?
The independent variable is not displayed
Along the y-axis
Along both the x- and y-axes
Sometimes along the x-axis and sometimes along the y-axis
Along the x-axis
Along the x-axis
The independent variable is controlled by the experimenter, while the dependent variable will fluctuate based on independent variable inputs. The independent variable is always displayed on the x-axis of a graph, while the dependent variable appears on the y-axis. Time is a common independent variable, as it will not be affeced by any dependent environemental inputs. Time can be treated as a controllable constant against which changes in a system can be measured.
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