Glossary
Acceleration
The instantaneous rate of change of an object's velocity with respect to time. It is the first derivative of the velocity function, $a(t) = v'(t)$, and the second derivative of the position function, $a(t) = x''(t)$.
Example:
If a rocket's velocity is , its acceleration at is units/time.
At Rest
A particle is considered at rest at any moment in time when its instantaneous velocity is equal to zero.
Example:
If a particle's velocity is , it is at rest when (for ).
Average Velocity
The total displacement of an object divided by the total time elapsed over a given interval. It is calculated as the change in position divided by the change in time.
Example:
If a runner's position changes from meters to meters, their average velocity from to is m/s.
Position Function
A function, typically denoted as $x(t)$ or $s(t)$, that gives the location of an object at any given time $t$.
Example:
If a particle's position function is , its location at is units.
Rectilinear Motion
Motion that occurs along a single straight line, often represented on an x-axis or y-axis.
Example:
A train moving along a straight track demonstrates rectilinear motion.
Slowing Down
An object is slowing down when its velocity and acceleration have opposite signs (one positive and one negative), meaning the magnitude of its velocity is decreasing.
Example:
A ball thrown upwards () experiences downward acceleration due to gravity (), causing it to slow down as it rises.
Speed
The magnitude (absolute value) of an object's velocity, indicating how fast it is moving without considering its direction.
Example:
If a particle's velocity is m/s, its speed is m/s.
Speeding Up
An object is speeding up when its velocity and acceleration have the same sign (both positive or both negative), meaning the magnitude of its velocity is increasing.
Example:
A car moving backward () with negative acceleration () is speeding up in the backward direction.
Velocity
The instantaneous rate of change of an object's position with respect to time, indicating both its speed and direction. It is the first derivative of the position function, $v(t) = x'(t)$.
Example:
If a car's position is given by , its velocity at is units/time.