Motion

Module 5, Lesson 1 | PHYS-1315 Physical Science I
"Nothing happens until something moves."
— Albert Einstein

Understanding Motion

Motion is everywhere around us - from the smallest atomic vibrations to the grandest movements of planets and galaxies. Understanding motion is fundamental to physics because it allows us to describe how objects change position, predict where they will be, and analyze the forces that cause these changes.

Whether it's a car accelerating down a highway, a baseball following a curved path through the air, or the Earth orbiting the Sun, all motion can be described using the same mathematical principles and physical concepts that form the foundation of kinematics.

Reference Frames

Motion is always relative - an object's motion depends on the reference frame from which it's observed. A passenger on a moving train appears stationary to other passengers but is moving to someone standing on the platform.

Learning Objectives

Course Competency CC5.1

Solve problems related to motion and kinematics

LO5.1.1

Compare and contrast the different types of motion, including uniform, accelerated, circular, and projectile motion.

LO5.1.2

Draw displacement, velocity, and acceleration vectors of moving objects to represent motion graphically.

LO5.1.3

Solve problems involving kinematic equations for various types of motion scenarios.

LO5.1.4

Draw and compute centripetal acceleration of an object undergoing uniform circular motion.

Required Readings

Primary Reading

Supplementary Resources

Interactive Activity 1: Motion Analysis Sequence

Instructions: Arrange the following steps in the correct order for analyzing any motion problem. This systematic approach helps ensure you consider all important aspects when studying motion.

Define the reference frame and coordinate system

Establish what you consider stationary and choose positive directions

Identify initial and final positions

Determine starting point and where the object ends up

Identify the time interval

Determine how long the motion takes or specific time points

Determine initial and final velocities

Find the speed and direction at the beginning and end

Identify acceleration (if any)

Determine if velocity is changing and at what rate

Choose appropriate kinematic equation

Select the equation that relates your known and unknown variables

Solve and verify the solution

Calculate the answer and check if it makes physical sense

Problem-Solving Key: Following this systematic approach helps avoid common mistakes and ensures you consider all relevant information. Remember that motion problems often have multiple valid approaches, but this sequence provides a reliable framework.

Interactive Activity 2: Motion Concepts Classification

Instructions: Sort the following motion-related concepts into their correct categories. Understanding these classifications helps in choosing the right approach for different types of motion problems.

Motion Types

Different categories of motion

Kinematic Variables

Quantities that describe motion

Key Equations

Mathematical relationships in kinematics

Real-World Examples

Common motion scenarios

Uniform motion (constant velocity)
Uniformly accelerated motion
Uniform circular motion
Projectile motion
Free fall motion
Displacement (Δx)
Velocity (v)
Acceleration (a)
Time (t)
Initial velocity (v₀)
v = v₀ + at
x = x₀ + v₀t + ½at²
v² = v₀² + 2a(x - x₀)
acentripetal = v²/r
Car accelerating from stop sign
Ball dropped from building
Satellite orbiting Earth
Baseball thrown horizontally

Motion Analysis: Each type of motion requires specific approaches and equations. Uniform motion uses simple distance = speed × time relationships, while accelerated motion requires kinematic equations. Circular motion introduces centripetal acceleration even when speed is constant.

Interactive Activity 3: Motion Principles and Equations

Instructions: Click each card to reveal detailed information about fundamental motion concepts, equations, and problem-solving strategies. These principles form the foundation of kinematics.

Displacement vs Distance

Vector vs Scalar

Understanding Position Changes

  • • Distance: Total path length traveled (scalar)
  • • Displacement: Straight-line change in position (vector)
  • • Displacement has magnitude and direction
  • • Distance is always positive; displacement can be negative
  • • For straight-line motion: |displacement| ≤ distance
  • • Symbol: Δx = x_final - x_initial

Velocity vs Speed

Rate of Motion

Describing How Fast

  • • Speed: Distance traveled per unit time
  • • Velocity: Displacement per unit time (has direction)
  • • Average velocity = Δx/Δt
  • • Instantaneous velocity = dx/dt
  • • Velocity can be negative (indicates direction)
  • • Speed is always non-negative

Acceleration

Change in Velocity

Rate of Velocity Change

  • • Acceleration = change in velocity / time
  • • a = (v - v₀)/t or a = Δv/Δt
  • • Positive acceleration can mean speeding up or slowing down
  • • Direction matters: acceleration opposite to velocity means slowing
  • • Units: m/s² or "meters per second squared"
  • • Zero acceleration = constant velocity

Kinematic Equation 1

v = v₀ + at

Velocity-Time Relationship

  • • Relates final velocity to initial velocity
  • • v: final velocity
  • • v₀: initial velocity
  • • a: acceleration
  • • t: time
  • • Use when you know acceleration and time
  • • Linear relationship between velocity and time

Kinematic Equation 2

x = x₀ + v₀t + ½at²

Position-Time Relationship

  • • Relates position to initial conditions and time
  • • x: final position
  • • x₀: initial position
  • • v₀t: displacement from initial velocity
  • • ½at²: displacement from acceleration
  • • Parabolic relationship for constant acceleration
  • • Most useful for finding position or time

Kinematic Equation 3

v² = v₀² + 2a(x - x₀)

Velocity-Position Relationship

  • • Independent of time (no t variable)
  • • Relates velocities to displacement
  • • Useful when time is unknown
  • • (x - x₀): displacement
  • • Often used for finding final velocity
  • • Can solve for any variable except time

Free Fall

g = 9.8 m/s²

Motion Under Gravity

  • • Special case of uniformly accelerated motion
  • • Acceleration = g = 9.8 m/s² downward
  • • Use kinematic equations with a = g
  • • Air resistance usually neglected
  • • Time up = time down for projectiles
  • • All objects fall at same rate (in vacuum)

Uniform Circular Motion

Centripetal Acceleration

Motion in a Circle

  • • Constant speed, changing velocity direction
  • • Centripetal acceleration = v²/r
  • • Acceleration points toward center
  • • v: tangential speed
  • • r: radius of circular path
  • • Period T = 2πr/v

Types of Motion

Uniform Motion

Definition: Motion at constant velocity (constant speed in a straight line).

Characteristics:

  • No acceleration (a = 0)
  • Equal distances in equal time intervals
  • Velocity vs. time graph is horizontal line
  • Position vs. time graph is straight line

Equation: x = x₀ + vt

Accelerated Motion

Definition: Motion with changing velocity (constant acceleration).

Characteristics:

  • Constant acceleration (a ≠ 0)
  • Velocity changes at constant rate
  • Velocity vs. time graph is straight line
  • Position vs. time graph is parabola

Key Equations: Kinematic equations 1-3

Circular Motion

Definition: Motion in a circular path at constant speed.

Characteristics:

  • Constant speed, changing direction
  • Acceleration toward center of circle
  • Acceleration magnitude = v²/r
  • Period T = 2πr/v

Examples: Satellites, car on curve, carousel

Projectile Motion

Definition: Motion of object under influence of gravity only.

Characteristics:

  • Horizontal velocity constant
  • Vertical acceleration = -g
  • Parabolic trajectory
  • Time up = time down

Examples: Thrown ball, fired cannonball

Video Lectures

Motion & Kinematics Introduction

Duration: 8 minutes | Topic: Motion types, coordinates, position

ASL Version available

Displacement, Velocity, and Speed

Duration: 5:40 | Topic: Vector arithmetic, velocity, acceleration

ASL Version available

Average vs Instantaneous Velocity

Duration: 17:59 | Topic: Kinematic equations, free fall, projectiles

ASL Version available

Uniform Circular Motion

Duration: 8:11 | Topic: Circular motion, Kepler's Laws

ASL Version available

Practice Problems

Problem 1: Uniform Motion

The driver of a car moving at 72.0 km/h drops a road map on the floor. It takes him 3.00 s to locate and pick up the map. How far did he travel during this time?
Click to reveal solution

Given: v = 72.0 km/h, t = 3.00 s

Convert units: 72.0 km/h × (1000 m/km) × (1 h/3600 s) = 20.0 m/s

For uniform motion: distance = velocity × time

Solution: d = 20.0 m/s × 3.00 s = 60.0 m

Video solution (18:36)

Problem 2: Acceleration

A bicycle moves from rest to 5 m/s in 5 s. What was the acceleration?
Click to reveal solution

Given: v₀ = 0 m/s, v = 5 m/s, t = 5 s

Use: a = (v - v₀)/t

Solution: a = (5 - 0)/5 = 1 m/s²

Video solution (9:54)

Problem 3: Free Fall

A rock that is dropped into a well hits the water in 3.0 s. Ignoring air resistance, how far is it to the water?
Click to reveal solution

Given: v₀ = 0 m/s, t = 3.0 s, a = g = 9.8 m/s²

Use: x = x₀ + v₀t + ½at²

Solution: x = 0 + 0 + ½(9.8)(3.0)² = ½(9.8)(9) = 44 m

Video solution (7:42)

PHYS-1315 Physical Science I | Module 5, Lesson 1

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