Motion — Position, Velocity, Acceleration

The relationship:

Position: s(t)

Velocity: v(t) = s'(t)

Acceleration: a(t) = v'(t) = s''(t)

Going backwards (integration):

v(t) = ∫a(t)dt

s(t) = ∫v(t)dt

Key concepts:

Speed = |v(t)| (always positive)

Object moving right/up when v(t) > 0

Object moving left/down when v(t) < 0

Object speeding up when v and a have same sign

Object slowing down when v and a have opposite signs

Total distance traveled: ∫ from a to b |v(t)| dt (not the same as displacement)

Displacement: ∫ from a to b v(t) dt = s(b) - s(a)

AP staple. Motion appears on free response almost every year.

Reference:

Wikipedia: Kinematics

https://en.wikipedia.org/wiki/Kinematics