Chapter 2: Motion in a Straight Line

Vocabulary flashcards covering the key concepts, definitions, and equations from Motion in a Straight Line. Each term is defined in the context of rectilinear motion with constant acceleration.

Instantaneous velocity

The velocity at a precise instant, defined as the limit of the average velocity as Δt → 0; equals dx/dt and is the slope of the position–time graph at that instant.

Velocity

The rate of change of position with respect to time; a vector quantity given by dx/dt, with magnitude and direction.

Average velocity

The change in position over a time interval, Δx/Δt; the slope of the line between two points on a position–time graph.

Instantaneous speed

The magnitude of instantaneous velocity; the speed at a specific instant (speed = |v|).

Speed

The scalar magnitude of velocity; instantaneous speed equals |v|, and average speed over an interval is typically ≥ the magnitude of the average velocity.

Acceleration

The average rate of change of velocity over a time interval, a = Δv/Δt; SI unit m s⁻²; equal to the slope of the velocity–time graph.

Instantaneous acceleration

The acceleration at a specific instant, a = dv/dt; the limit of average acceleration as Δt → 0; slope of the velocity–time graph at that instant.

Uniform (constant) acceleration

Acceleration that does not change with time; velocity–time graph is a straight line, and the x–t graph is a parabola.

Kinematic equations (constant acceleration)

v = v0 + a t; x = x0 + v0 t + (1/2) a t²; v² = v0² + 2 a (x − x0); relate displacement, time, initial/final velocity, and acceleration for one‑dimensional motion.

Displacement

The change in position, x − x0, a vector quantity; depends on the path but is defined by the difference in positions.

Area under the velocity–time curve

The integral of velocity over a time interval; equals the displacement during that interval.

Position–time graph

A plot of position x versus time t; its slope gives instantaneous velocity and its curvature relates to acceleration.

Velocity–time graph

A plot of velocity v versus time t; its slope gives acceleration and the area under the curve gives displacement.

Free fall

Motion under gravity with negligible air resistance; acceleration a = −g (downward, g ≈ 9.8 m s⁻²); described by v = −g t and y = −(1/2) g t² (with upward as positive).

Stopping distance

Distance travelled before coming to rest; derived from v² = v0² + 2 a x with v = 0; shows stopping distance ∝ v0² for constant deceleration.

Reaction time

Time between perceiving a situation and initiating a response; can be measured experimentally (e.g., ruler drop test).

Galileo’s law of odd numbers

In free fall from rest, distances fallen in successive equal time intervals are in the ratio 1:3:5:7…; a consequence of constant acceleration.

Point object approximation

Treating an extended body as a point when its size is negligible compared to the distance traveled; valid in many rectilinear motion analyses.

Rectilinear motion

Motion along a straight line; the focus of this chapter’s analysis using velocity and acceleration.

Sign convention for axes

Before assigning signs to displacement, velocity, and acceleration, specify the positive direction and origin; the sign of acceleration depends on this choice.

v0 and x0

v0 is the initial velocity at t = 0; x0 is the initial position at t = 0; used in the kinematic equations to set initial conditions.