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What is the difference between average and instantaneous velocity?
Average velocity: Velocity over a time interval. | Instantaneous velocity: Velocity at a specific moment.
How do average and instantaneous values relate as the time interval approaches zero?
As the time interval approaches zero, average values converge to instantaneous values.
Differentiate between distance and displacement.
Distance: Total path length traveled. | Displacement: Change in position from start to finish.
Compare and contrast velocity and acceleration.
Velocity: Rate of change of displacement (speed with direction). | Acceleration: Rate of change of velocity.
What's the difference between constant velocity and no velocity?
Constant Velocity: Object is moving at a steady rate in a straight line. | No Velocity: Object is at rest.
What is the effect of a changing velocity?
Acceleration occurs.
What is the effect of integrating an acceleration function with respect to time?
The change in velocity is obtained.
What is the effect of integrating a velocity function with respect to time?
The displacement is obtained.
What happens when the time interval approaches zero when calculating average velocity?
Average velocity approaches instantaneous velocity.
What happens when the time interval approaches zero when calculating average acceleration?
Average acceleration approaches instantaneous acceleration.
What is displacement ($\Delta \vec{x}$)?
The change in position of an object; a vector quantity with magnitude and direction.
What is average velocity ($\vec{v}_{avg}$)?
The displacement of an object over a time interval: $\vec{v}_{avg} = \frac{\Delta \vec{x}}{\Delta t}$.
What is average acceleration ($\vec{a}_{avg}$)?
The change in velocity of an object over a time interval: $\vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t}$.
What is instantaneous velocity ($\vec{v}$)?
The derivative of position with respect to time: $\vec{v} = \frac{d\vec{r}}{dt}$.
What is instantaneous acceleration ($\vec{a}$)?
The derivative of velocity with respect to time: $\vec{a} = \frac{d\vec{v}}{dt}$.