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Lesson 1: Describing Motion with Words

Introduction to the Language of Kinematics

Scalars and Vectors

Distance and Displacement

Speed and Velocity

Acceleration


Lesson 2: Describing Motion with Diagrams

Introduction to Diagrams

Ticker Tape Diagrams

Vector Diagrams


Lesson 3: Describing Motion with Position vs. Time Graphs

The Meaning of Shape for a p-t Graph

The Meaning of Slope for a p-t Graph

Determining the Slope on a p-t Graph


 

Lesson 4: Describing Motion with Velocity vs. Time Graphs

The Meaning of Shape for a v-t Graph

The Meaning of Slope for a v-t Graph

Relating the Shape to the Motion

Determining the Slope on a v-t Graph

Determining the Area on a v-t Graph

 

Lesson 5: Free Fall and the Acceleration of Gravity

Introduction to Free Fall

The Acceleration of Gravity

Representing Free Fall by Graphs

How Fast? and How Far?

The Big Misconception

 

Lesson 6: Kinematic Equations

The Kinematic Equations

Problem-Solving

Kinematic Equations and Free Fall

Sample Problems and Solutions

Kinematic Equations and Graphs

 

 

Lesson 4 : Describing Motion with Velocity vs. Time Graphs

Determining the Slope on a v-t Graph

It was learned earlier in Lesson 4 that the slope of the line on a velocity versus time graph is equal to the acceleration of the object. If the object is moving with an acceleration of +4 m/s/s (i.e., changing its velocity by 4 m/s per second), then the slope of the line will be +4 m/s/s. If the object is moving with an acceleration of -8 m/s/s, then the slope of the line will be -8 m/s/s. If the object has a velocity of 0 m/s, then the slope of the line will be 0 m/s. Because of its importance, a student of physics must have a good understanding of how to calculate the slope of a line. In this part of the lesson, the method for determining the slope of a line on a velocity-time graph will be discussed.

Let's begin by considering the velocity versus time graph below.

The line is sloping upwards to the right. But mathematically, by how much does it slope upwards for every 1 second along the horizontal (time) axis? To answer this question we must use the slope equation.

The slope equation says that the slope of a line is found by determining the amount of rise of the line between any two points divided by the amount of run of the line between the same two points. A method for carrying out the calculation is

  1. Pick two points on the line and determine their coordinates.
  2. Determine the difference in y-coordinates for these two points (rise).
  3. Determine the difference in x-coordinates for these two points (run).
  4. Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

 

The diagram below shows this method being applied to determine the slope of the line. Note that three different calculations are performed for three different sets of two points on the line. In each case, the result is the same: the slope is 10 m/s/s.

 

Observe that regardless of which two points on the line are chosen for the slope calculation, the result remains the same - 10 m/s/s.

 

 

Check Your Understanding

Consider the velocity-time graph below. Determine the acceleration (i.e., slope) of the object as portrayed by the graph. Click the button to check your answer.

 

 

 

 

 

 

Lesson 4 : Describing Motion with Velocity vs. Time Graphs

 

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