AP Physics C: Mechanics — Unit 1: Kinematics Breakdown

Position ($x$)

The location of an object relative to a defined origin at a specific time.

Displacement ($$)

The change in position of an object; a vector quantity.

Distance

The total path length traveled by an object; a scalar quantity.

Average Velocity ($v_{avg}$)

Total displacement divided by the time interval.

Instantaneous Velocity ($v$)

The velocity at a specific moment, defined as the derivative of position with respect to time.

Speed

The magnitude of the instantaneous velocity vector; a scalar.

Average Acceleration ($a_{avg}$)

The change in velocity over a time interval.

Instantaneous Acceleration ($a$)

The rate of change of velocity; derivative of velocity or second derivative of position.

Kinematic Equations

Equations used to describe motion with constant acceleration.

Free Fall

The motion of an object under the influence of gravitational force alone.

Acceleration due to gravity ($g$)

The constant acceleration of an object in free fall near Earth’s surface, approximately 9.8 m/s².

Kinematic Equation: $vx = v{x0} + a_xt$

Describes relationships between final and initial velocity, acceleration, and time.

Kinematic Equation: $x = x0 + v{x0}t + \frac{1}{2}a_xt^2$

Gives the position of an object in terms of initial position, initial velocity, time, and constant acceleration.

Kinematic Equation: $vx^2 = v{x0}^2 + 2ax(x - x0)$

Relates final velocity to initial velocity, acceleration, and change in position.

Integration

A mathematical process used to find quantities like velocity and position from acceleration.

Area under the curve

In a velocity vs. time graph, represents displacement; in an acceleration vs. time graph, represents change in velocity.

Jerk

The rate of change of acceleration; slope of acceleration vs. time graph.

Initial Condition

A known value at the start of a problem, used to solve for constants of integration.

Sign Convention

A consistent definition of positive and negative directions in a coordinate system.

Scalar Quantity

A physical quantity that has magnitude only and no direction.

Vector Quantity

A physical quantity that has both magnitude and direction.

Derivative

A mathematical operation that determines the rate at which one quantity changes with respect to another.

Constant Acceleration

Motion where the acceleration is the same throughout the time period considered.

Displacement vs. Distance

Displacement is the change in position and can be zero; distance is the total path length and is never negative.

Initial Velocity ($v_{x0}$)

The velocity of an object at the start of the observation period.

Changing Acceleration

When acceleration varies with time or position, requiring calculus to solve.