Location of an object in space at time $t$.

Rate of change of position with respect to time; $v(t) = s'(t)$.

Rate of change of velocity with respect to time; $a(t) = v'(t) = s''(t)$.

Change in position: $\Delta s = s_f - s_i$.

Total length of the path an object takes.

Magnitude of the velocity; absolute value of velocity.

The position of an object at time $t=0$, denoted as $s(0)$.

The velocity of an object at time $t=0$, denoted as $v(0)$.

Velocity is the derivative of position with respect to time.

Acceleration is the derivative of velocity with respect to time.

Integrating $v(t)$ gives the change in position (displacement). Add the initial position to find the final position.

Integrating $a(t)$ gives the change in velocity. Add the initial velocity to find the final velocity.

The area under the $v(t)$ curve represents the displacement of the object.

The area under the $|v(t)|$ curve represents the total distance traveled by the object.

It accounts for changes in direction, ensuring all movement contributes positively to the total distance.

C represents the initial condition (position or velocity) needed to find the specific function.

The slope of the position vs. time graph at any point gives the velocity at that time.

The slope of the velocity vs. time graph at any point gives the acceleration at that time.

The object is at rest; its velocity is zero.

The object is moving at a constant velocity; its acceleration is zero.

Displacement: Change in position, can be negative | Distance Traveled: Total path length, always non-negative.

Velocity: Rate of change of position with direction (can be negative) | Speed: Magnitude of velocity (always non-negative).

Definite Integral: Directly calculates displacement over an interval | Indefinite Integral: Gives a general position function, requires initial position to find displacement.

Derivatives: Find velocity from position function | Integrals: Find velocity from acceleration function.

Average Velocity: Displacement over a time interval | Instantaneous Velocity: Velocity at a specific moment in time.

Positive Acceleration: Velocity is increasing | Negative Acceleration: Velocity is decreasing (deceleration).

Constant Velocity: Acceleration is zero, object moves at a steady rate | Constant Acceleration: Velocity changes at a steady rate.

v(t) > 0: Displacement is positive, object moves in positive direction | v(t) < 0: Displacement is negative, object moves in negative direction.

Zero Velocity: Object is momentarily at rest | Zero Acceleration: Velocity is constant.

Initial Position: Used to find the constant of integration when integrating velocity | Initial Velocity: Used to find the constant of integration when integrating acceleration.