Chapter 9, "Derivative Approach to Motion in One Dimension"

Average Velocity

equals the slope between two points on position v. Time graph for any time interval a t b.

Instantaneous Velocity

at t = a for any function f(t) that gives position as a function of time.

Instantaneous Velocity

v = f'(t)

for any position equation that's a function of time, f(t).

Average Acceleration

equals the slope between two points on velocity v. Time graph for any time interval a t b.

Instantaneous Acceleration

for any function f(t) that gives velocity as a function of time.

Instantaneous Acceleration

a = v'(t)

for any velocity equation that's a function of time, v(t).

Instantaneous Acceleration

a = v'(t) = y''(t)

for any velocity equation that's a function of time, v(t), and any position equation that's a function of time, y(t).