Glossary

Acceleration

Criticality: 3

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 $v(t) = 5t^2 - 3t$ , its acceleration at $t=2$ is $a(2) = 10(2) - 3 = 17$ units/time $^2$ .

At Rest

Criticality: 2

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 $v(t) = t^2 - 4$ , it is at rest when $t=2$ (for $t \ge 0$ ).

Average Velocity

Criticality: 2

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 $x(1)=2$ meters to $x(5)=18$ meters, their average velocity from $t=1$ to $t=5$ is $(18-2)/(5-1) = 16/4 = 4$ m/s.

Position Function

Criticality: 3

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 $x(t) = t^2 - 4t$ , its location at $t=5$ is $x(5) = 5^2 - 4(5) = 5$ units.

Rectilinear Motion

Criticality: 2

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

Criticality: 3

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 ( $v(t) > 0$ ) experiences downward acceleration due to gravity ( $a(t) < 0$ ), causing it to slow down as it rises.

Speed

Criticality: 3

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 $v(t) = -10$ m/s, its speed is $|-10| = 10$ m/s.

Speeding Up

Criticality: 3

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 ( $v(t) < 0$ ) with negative acceleration ( $a(t) < 0$ ) is speeding up in the backward direction.

Velocity

Criticality: 3

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 $x(t) = 3t^2 + 2t$ , its velocity at $t=1$ is $v(1) = 6(1) + 2 = 8$ units/time.

Glossary

Acceleration

Criticality: 3

Example:

If a rocket's velocity is $v(t) = 5t^2 - 3t$ , its acceleration at $t=2$ is $a(2) = 10(2) - 3 = 17$ units/time $^2$ .

At Rest

Criticality: 2

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 $v(t) = t^2 - 4$ , it is at rest when $t=2$ (for $t \ge 0$ ).

Average Velocity

Criticality: 2

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 $x(1)=2$ meters to $x(5)=18$ meters, their average velocity from $t=1$ to $t=5$ is $(18-2)/(5-1) = 16/4 = 4$ m/s.

Position Function

Criticality: 3

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 $x(t) = t^2 - 4t$ , its location at $t=5$ is $x(5) = 5^2 - 4(5) = 5$ units.

Rectilinear Motion

Criticality: 2

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

Criticality: 3

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 ( $v(t) > 0$ ) experiences downward acceleration due to gravity ( $a(t) < 0$ ), causing it to slow down as it rises.

Speed

Criticality: 3

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 $v(t) = -10$ m/s, its speed is $|-10| = 10$ m/s.

Speeding Up

Criticality: 3

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 ( $v(t) < 0$ ) with negative acceleration ( $a(t) < 0$ ) is speeding up in the backward direction.

Velocity

Criticality: 3

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 $x(t) = 3t^2 + 2t$ , its velocity at $t=1$ is $v(1) = 6(1) + 2 = 8$ units/time.