Particle Motion (Calculus)

A particle is at rest when its velocity, v(t), is equal to 0.

A particle has negative velocity if its position graph is decreasing.

Speed is the magnitude of velocity, represented as |v(t)|.

A particle has positive velocity if its position graph is increasing.

A particle's speed is decreasing if its velocity and acceleration have different signs.

Acceleration is the rate of change of velocity with respect to time, denoted as a(t).

The derivative of position, x'(t), represents the velocity of the particle.

Instantaneous velocity is the velocity of a particle at a specific moment in time, calculated as the derivative of position.

Positive acceleration indicates that the particle's velocity is increasing.

Negative acceleration indicates that the particle's velocity is decreasing.