Motion

Quick Notes

• For this category, we are looking at particles (or people, bugs, cars, or turtles) moving in a straight line. This is often along the x- or y-axis.

• A motion question is always on the AB exam, and the BC exam almost always has either 1D or 2D motion.

• Usually, you are given velocity, but you may be given position or acceleration instead. Typically, initial conditions are given as well.

• The given information could be in the form of equations, graphs, or tables. Therefore, analysis regarding any of the three representations is fair game.

• These questions can be very similar to accumulation problems, just with a specific context.

• Velocity is the derivative of position [v(t) = s'(t)], and acceleration is the derivative of velocity [a(t) = v'(t) = s''(t)].

• Speed is the absolute value of the velocity.

• An object is speeding up if velocity and acceleration have the same sign, and an object is slowing down if velocity and acceleration have opposite signs.

• The position at any time can be found using FTC with velocity; simply add the displacement to the initial position.

• The displacement is the net change of position and can be found by integrating velocity.

• Distance Traveled can be found by integrating speed (absolute value of velocity).

• You may be asked to find average velocity, acceleration, or speed. Make sure you know whether to use Average Rate or Average Value. When in doubt, check your units.

• You might need to calculate a maximum or minimum value, but it often won't directly state "maximum" or "minimum" and will use phrases specific to motion.

• You may need to approximate derivative or integral values from a table using AROC or Riemann Sums respectively.

• Similar to approximation questions, these questions might ask you to interpret the meaning of something in context. Remember to include "NUT" (Number, Units, Time).

• On the BC exam, questions  may be regarding 2D motion with Parametric & Vectors.

~ Related CED Units ~ 4, 5, 6, 8

FRQ Samples

2024 AB 2

2023 AB 2

2022 AB 6

2021 AB 2

2019 AB 2

2018 AB 2

2017 AB 5

2009 AB 1 / BC 1

~ Reference Sheet ~

Particle Motion

Created by Bryan Passwater.