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Instantaneous velocity and speed from graphs review

Review the key terms and skills related to analyzing motion graphs, such as finding velocity from position vs. time graphs and displacement from velocity vs. time graphs.

Key terms

Instantaneous velocityVelocity at a given moment in time. Has SI units of ms.
Instantaneous speedSpeed at a given moment in time. Equal to the magnitude of the instantaneous velocity. Has SI units of ms.
EquationSymbol breakdownMeaning in words
v¯=ΔxΔtv¯ is average velocity, Δx is displacement, and Δt is change in time.Average velocity is displacement divided by time interval of displacement.
vavg=dΔtvavg is average speed, d is distance, and Δt is change in time .Average speed is distance divided by time interval for the distance traveled.

Analyzing motion graphs

Velocity is the slope of position vs. time graph

The equation for the slope of a position vs. time graph matches the definition of velocity exactly.
To calculate the average velocity between two points P1 and P2, we divide the change of position Δx by the change in time Δt.
The instantaneous velocity at point P1 is equal to the slope of the position graph at point P1.

Displacement is the area under the curve on a velocity vs. time graph

To find the displacement between two points P1 and P2 on a velocity vs. time graph, we find the area under the curve between the two points.
The change in time Δt will be the width of the area, and the height v is on the vertical axis.

Common mistakes and misconceptions

Some people think instantaneous velocity and speed are the same as average velocity and speed. When people use the words speed or velocity, they usually mean instantaneous velocity or instantaneous speed. Average velocity and speed account for motion occurring over a time period, and instantaneous velocity and speed describe motion at a given moment in time.

Learn more

For deeper explanations of velocity and speed see the videos on instantaneous speed and velocity and position vs. time graphs.
To check your understanding and work toward mastering these concepts, check out these exercises:

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