Basic Rate of Change Ideas
The average rate of change of A with respect to B is
- average rate = change in A / change in B
The following are rate of change ideas essential to physics:
- Frequency is the rate at which things occur with respect to
clock time.
- Velocity is the rate at which position changes with respect
to clock time.
- Acceleration is the rate at which velocity changes with
respect to clock time.
- Net force is the rate at which momentum changes with
respect to clock time.
- Net force is the rate at which work changes with respect to
distance.
Position is measured with respect to a coordinate line or a
coordinate plane, and change in position is called displacement:
- For an object moving along a
straight line, position is measured on a coordinate axis.
- For an object moving on a
2-dimensional plane position is measured on a coordinate plane.
- For an object moving in
3-dimensional space position
is measure on a 3-dimensional coordinate plane.
- Change in position is
displacement. The magnitude of change in position is distance.
Change in position, change in velocity
and change in acceleration are all vector quantities, meaning they have
magnitude (the number of units by which the quantity changes) and direction
(e.g., it makes a big difference whether your car is moving forward or backward,
and whether it is accelerating in the forward or backward direction or perhaps
in some other direction)..
University Physics:
By the Fundamental Theorem of Calculus:
- Change in position is the definite integral of velocity
with respect to clock time.
- Change in velocity is the definite integral of acceleration
with respect to clock time.
- Momentum is the definite integral of force with respect to
clock time.
- Work is the definite integral of force with respect to
distance.
Note also that the proportion of one quantity to another is
proportion = first quantity / second quantity
and to express one quantity as a percent of the other we
multiply the proportion by 100%.
Speed is | velocity |.