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Initially
t = 0
At rest
v(t) = 0
Particle moving right (forward)
v(t) > 0
Particle moving left (backward)
v(t) < 0
Average velocity on [a, b]
s(b) - s(a) / b - a
Instantaneous velocity at time t
v(t) = s’(t)
Acceleration at time t
a(t) = v’(t) = s’’(t)
Velocity is increasing
a(t) = v’(t) > 0
Velocity is decreasing
a(t) = v’(t) < 0
Speed
|v(t)|
Speed is increasing (accelerating)
v(t) and a(t) have the same signs
Speed is decreasing (decelerating)
v(t) and a(t) have the different signs
Particle is farthest left (right)
Compare positions (x-values) at endpoint and at relative minima/maxima