Speed, Velocity, and Acceleration
From Distance to Change in Motion
Speed versus velocity
Speed tells how fast something moves and has no direction. Velocity tells how fast and in what direction something moves. In one dimension, velocity can be positive or negative.
Average and instantaneous quantities
Average velocity is . Average speed is total distance divided by total time. Instantaneous velocity is the velocity at a specific moment.
Acceleration
Acceleration is the rate at which velocity changes: . If acceleration is positive, velocity may increase in the positive direction. If it is negative, velocity may decrease or become more negative, depending on direction.
Important distinction
An object can have zero velocity and still have nonzero acceleration, such as at the top of a thrown ball’s path.
Speed vs. velocity
Speed
- Scalar quantity
- No direction
- Uses total distance over time
Velocity
- Vector quantity
- Has direction
- Uses displacement over time
If an object moves east at , what describes its velocity best?
Velocity includes both magnitude and direction.
Correct answer: east
What is the formula for average velocity in one dimension?
Average velocity is displacement divided by elapsed time.
Correct answer: v_avg = Δx / Δt
Reading motion problems
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Step 1: Identify whether the problem asks about speed, velocity, or acceleration.
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Step 2: Note whether direction matters.
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Step 3: Use displacement for velocity and distance for speed.
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Step 4: Check units carefully.