Velocity: a vector quantity with magnitude and direction. Speed: a scalar quantity representing the magnitude of velocity.

Displacement: change in position (can be negative). Total Distance: total length traveled (always non-negative).

Average Velocity: Velocity over an interval. Instantaneous Velocity: Velocity at a specific time.

Positive acceleration: velocity increasing in the positive direction. Negative acceleration: velocity increasing in the negative direction.

Speeding up: velocity and acceleration have the same sign. Slowing down: velocity and acceleration have opposite signs.

Velocity: rate of change of position. Acceleration: rate of change of velocity.

$v(t) = x'(t) = \frac{dx}{dt}$

$a(t) = v'(t) = \frac{dv}{dt}$

$a(t) = x''(t) = \frac{d^2x}{dt^2}$

$\frac{x(b) - x(a)}{b - a}$

$v(c) = x'(c)$

$a(c) = v'(c) = x''(c)$

$x(t) = \int v(t) dt$

$v(t) = \int a(t) dt$

$\int_{a}^{b} v(t) dt$

$\int_{a}^{b} |v(t)| dt$

Rate of change of position with respect to time; the derivative of position, $v(t) = x'(t)$.

The magnitude (absolute value) of velocity; how fast something is moving, $|v(t)|$.

Rate of change of velocity with respect to time; the derivative of velocity, $a(t) = v'(t) = x''(t)$.

Motion along a straight line.

The position of an object at time $t$.

The velocity of an object at time $t$.

The acceleration of an object at time $t$.

The object is moving to the left or in the negative direction.

The object is moving to the right or in the positive direction.

The object is moving at a constant velocity.