Define displacement, velocity and acceleration as vector rates of change, distinguish them from distance and speed, and calculate average velocity and average acceleration from change in position and velocity over time.

What this topic is asking

This dot point defines the three core kinematic quantities, displacement, velocity and acceleration, as vector rates of change, and asks you to tell them apart from the scalars distance and speed. The Regents tests this two ways: conceptual multiple-choice items that hinge on the distance-versus-displacement or speed-versus-velocity distinction, and constructed-response calculations of average velocity or average acceleration using the equations printed on the Reference Tables.

Displacement versus distance

The two are equal only for motion in a straight line that never reverses. A runner who completes one lap of a track covers a large distance but has zero displacement, because they end where they began. On the Regents, the giveaway word is "displacement" or a phrase like "how far from the start", which signals the vector.

Velocity versus speed

Average velocity uses the displacement, so a runner who returns to the start has zero average velocity over the lap even though their average speed was high. Instantaneous velocity is the velocity at a single instant; on the Regents, "velocity" usually means the constant or average velocity unless a graph shows it changing.

Acceleration

A crucial Regents idea is that an object accelerates whenever its velocity vector changes in any way: when it speeds up, when it slows down (acceleration opposite to motion, sometimes called deceleration), or when it changes direction at constant speed (as in circular motion). A car rounding a bend at a steady speedometer reading is accelerating, because its direction, and therefore its velocity, is changing.

Calculating average velocity and acceleration

The two rate equations on the Reference Tables are the workhorses here. To find an average velocity, divide the displacement by the time; to find an average acceleration, divide the change in velocity by the time. Always keep track of direction with a sign: choosing one direction as positive lets a negative answer signal motion or acceleration the other way.

Reference Tables note

The Reference Tables for Physical Setting/Physics print both $\bar{v} = \dfrac{d}{t}$ and $\bar{a} = \dfrac{\Delta v}{\Delta t}$ in the Mechanics list, so you do not memorize them, but you must know that $d$ here means displacement and that a sign carries the direction. The constant-acceleration kinematic equations ($v_f = v_i + at$, etc.) are also printed and are treated in the kinematic equations.

Try this

Q1. State whether each is a scalar or a vector: distance, displacement, speed, velocity, acceleration. [2 points]

• Cue. Scalars: distance, speed. Vectors: displacement, velocity, acceleration.

Q2. An object's displacement is $60$ m north in $12$ s. Calculate its average velocity. [2 points]

• Cue. $\bar{v} = \dfrac{\Delta d}{\Delta t} = \dfrac{60}{12} = 5.0$ m/s north.