Kinematics in One Dimension

Vocabulary flashcards covering key terms from the notes on Kinematics in One Dimension.

Displacement (Δx)

The change in position of a particle along the x-axis, equal to xf − xi; can be positive or negative depending on direction; not the same as distance traveled.

Distance traveled

The total length of the path traveled by the particle; always positive and generally greater than or equal to the magnitude of displacement.

Position (x)

The location of a particle along the x-axis; x(t) denotes position as a function of time; xo is the initial position.

Initial position (x0)

The starting coordinate of the particle on the x-axis.

Final position (xf)

The ending coordinate of the particle on the x-axis at time t.

Average velocity (v̄)

Displacement divided by the elapsed time: v̄ = Δx/Δt; depends only on start and end coordinates; can be negative.

Instantaneous velocity (v)

The velocity at a specific instant; the limit of Δx/Δt as Δt → 0; equals dx/dt; can be positive, negative, or zero.

Velocity

The rate of change of position; a vector quantity with magnitude (speed) and direction.

Speed

The magnitude of velocity; a scalar; has no direction.

Acceleration (a)

The rate of change of velocity; a = dv/dt; units m/s²; can be positive or negative.

Instantaneous acceleration

The acceleration at a specific instant; dv/dt as Δt → 0; the time-rate of change of velocity.

Average acceleration (ā)

Change in velocity over a given time interval: ā = Δv/Δt.

Constant acceleration

Acceleration that does not vary with time; allows use of the standard kinematic equations.

Kinematic equations (constant acceleration)

Equations relating x, v, v0, a, t, and x0 for motion with constant acceleration; examples include v = v0 + a t and x = x0 + v0 t + (1/2) a t².

Position-time graph

Plot of position x versus time t; slope gives velocity; tangent slope gives instantaneous velocity; area under v–t curve equals displacement.

Velocity-time graph

Plot of velocity v versus time t; slope gives acceleration; area under the curve equals displacement.

Space-time graph

Graph of position versus time; the slope of the line between initial and final points equals velocity.

Free fall

Motion near Earth's surface under gravity only; acceleration is constant downward with g ≈ 9.8 m/s².

Gravity (g)

Acceleration due to gravity near Earth's surface, approximately 9.8 m/s² downward.

Derivative relationship for instantaneous velocity

Instantaneous velocity equals the derivative of position with respect to time: v = dx/dt.