PHYS 206 - Chapter 2: Motion Along a Straight Line (Vocabulary Flashcards)

Vocabulary flashcards covering key concepts from Chapter 2: Motion along a straight line, including displacement, distance, velocity, speed, acceleration, constant acceleration, and the fundamental equations of motion.

Displacement

A vector describing the straight-line change in position from initial to final: Δr = rf − ri; does not necessarily equal the distance traveled.

Distance

The total length of the path traveled; a scalar quantity.

Position vector (r)

The location of a particle in space, with components (x, y, z); r = x î + y ĵ + z k̂; can be written as r = (rx, ry, rz).

Average velocity

Displacement per unit time over a time interval: v_avg = Δr/Δt; a vector; components: vx = Δx/Δt, vy = Δy/Δt, vz = Δz/Δt.

Instantaneous velocity

The rate of change of position at a specific time t; limits Δt→0 of Δr/Δt; equal to dr/dt; slope of the x vs t curve at t.

Velocity

The rate of change of position; a vector whose magnitude is speed.

Speed

The magnitude of velocity; a scalar quantity.

Average acceleration

Change in velocity over a time interval divided by that interval: a_avg = Δv/Δt; a vector; a = dv/dt.

Instantaneous acceleration

The rate of change of velocity at a specific time; limit Δt→0 of Δv/Δt; equal to dv/dt; equals the slope of the v vs t curve.

Acceleration

The rate of change of velocity per unit time; a vector; units m/s^2; a = dv/dt = d^2r/dt^2.

Constant acceleration

Acceleration that remains the same over time; leads to the standard equations of motion.

Equations of motion (constant acceleration)

Relationships describing motion when a is constant: v(t) = v0 + a t; r(t) = r0 + v0 t + 1/2 a t^2; v^2 = v0^2 + 2 a (r − r0); r − r0 = 1/2 (v0 + v) t.

v(t) = v0 + a t

Velocity as a function of time for constant acceleration.

r(t) = r0 + v0 t + 1/2 a t^2

Position as a function of time for constant acceleration.

v^2 = v0^2 + 2 a (r − r0)

A kinematic relation relating velocities and displacement for constant acceleration.

r − r0 = 1/2 (v0 + v) t

Another form of the position-velocity-time relationship for constant acceleration.

Free fall

Vertical motion near Earth's surface with acceleration due to gravity: a = −g ĵ; g = 9.80 m/s^2.

g (acceleration due to gravity)

Magnitude of the acceleration g = 9.80 m/s^2 directed downward (−ĵ) near Earth’s surface.

x–t graph slope

The slope of the position vs. time graph equals the average velocity over that interval.

Instantaneous velocity on an x–t graph

The slope of the tangent to the x–t curve at time t; equals instantaneous velocity.