Average and Instantaneous Velocity
Average velocity is displacement divided by the time interval; instantaneous velocity is the limit of that ratio as the interval tends to zero, v = dx/dt.
What is Average and Instantaneous Velocity?
Average velocity is displacement divided by the time interval; instantaneous velocity is the limit of that ratio as the interval tends to zero, v = dx/dt.
Key formula / rule: vavg = Dx/Dt, vinst = dx/dt (slope of x-t graph).
Key points
- Distinguish average velocity from instantaneous velocity using an x-t graph.
- Compute average velocity and average speed for a multi-leg journey.
Common exam trap
Averaging two velocities arithmetically when the two legs take different ×.
Definitions
- Term
Average and Instantaneous Velocity
- Meaning
Average velocity is displacement divided by the time interval; instantaneous velocity is the limit of that ratio as the interval tends to zero, v = dx/dt.
- Term
Average and Instantaneous Velocity — explanation
- Meaning
Average velocity compresses a whole interval into one number and can be zero even when the body moved. Instantaneous velocity is the slope of the position-time graph at a point, which is what a speedometer approximates.
Learning objectives
Distinguish average velocity from instantaneous velocity using an x-t graph.
Compute average velocity and average speed for a multi-leg journey.
Formulae
- Key point
vavg = Dx/Dt, vinst = dx/dt (slope of x-t graph).
- Key point
Average speed uses distance, so it can exceed |average velocity|.
- Key point
A horizontal x-t graph means the body is at rest.
Prerequisites
PHY-U1-KIN-T1-S1-C1
Common mistakes
Averaging two velocities arithmetically when the two legs take different ×.
Reading the value of x instead of the slope of x-t as velocity.
Keywords
Average
Instantaneous
Velocity
Practice preview
What is the definition of average velocity?…
easy
How is instantaneous velocity defined?…
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A car travels 100 meters east in 10 seconds. What is its average velocity?…
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