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How do you find instantaneous velocity from a position function?
Take the derivative of the position function with respect to time: $v(t) = \frac{dx(t)}{dt}$.
How do you find instantaneous acceleration from a velocity function?
Take the derivative of the velocity function with respect to time: $a(t) = \frac{dv(t)}{dt}$.
How do you find displacement from a velocity function?
Integrate the velocity function with respect to time over the desired time interval: $\Delta x = \int_{t_1}^{t_2} v(t) dt$.
How do you find velocity from an acceleration function?
Integrate the acceleration function with respect to time over the desired time interval: $\Delta v = \int_{t_1}^{t_2} a(t) dt$.
What is the process for simplifying objects in kinematics?
Model objects as point particles, ignoring size and shape, and focusing on mass and charge.
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 the effect of a changing velocity?
The object experiences acceleration.
What happens when there is a constant velocity?
Acceleration is zero.
What is the effect of a non-zero acceleration?
The velocity of the object changes (either in magnitude or direction).
What is the effect of an object changing direction?
The object is accelerating, even if its speed is constant.
What is the effect of an object speeding up?
The object is accelerating.