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Describing Motion with Velocity vs. Time Graphs

Student Extras

The Physics Classroom: 1-D Problems

Improve your problem-solving skills with problems, answers and solutions from The Calculator Pad.

Flickr Physics

Visit The Physics Classroom's Flickr Galleries and take a visual overview of 1D Kinematics.

Shockwave Studios

For an interactive challenge, try the Two Stage Rocket activity from the Shockwave Studios.

Teacher's Guide

Shockwave Studios

Graphing Motion from the Shockwave Studios is an excellent accompanying activity to this page.

Shockwave Studios

Give your students a challenge with the Two Stage Rocket activity from the Shockwave Studios.

Curriculum Corner

Learning requires action. Give your students this sense-making activity from The Curriculum Corner.

Treasures from TPF

Need ideas? Explore The Physics Front's treasure box of catalogued resources on kinematic graphing.

Curriculum Corner

Help your students put their learning to practice with this sense-making activity from The Curriculum Corner.

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.