# Distance-Time and Velocity-Time Graphs: A Compact Presentation of Information

**Topics:**Curve, Analytic geometry, Linear equation

**Pages:**7 (1277 words)

**Published:**February 17, 2013

Graphing the motion of objects gives us a way to interpret the motion that would otherwise be difficult. ● Graphs will also allow you to show a large amount of information in a compact way. Essentially you need to be able to sketch and interpret two main kinds of graphs in kinematics: 1. Displacement – Time Graphs

● Sometimes called d-t graphs, or position – time graphs. 2. Velocity – Time Graphs

● Sometimes called v-t graphs.

Displacement - Time (d-t) Graphs

This type of graph is based on the most basic things we need to know about the motion of an object (position and time).

● Typically you will be given a table of values that show the displacement of the object over a particular period of time.

● If the graph shows complex motion (such as Illustration 1 below), you do not just draw a single best fit line. Instead, you need to look at each section of motion and determine what kind of line best fits the data.

● Don't worry too much about sketching these complex situations... it is much more likely that you will draw an object moving in one way only.

● For the example graph shown below, imagine that you are running in a marathon, and we have decided to graph your movement.

Illustration 1: d-t graph of a person running a marathon.

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© studyphysics.ca

Page 1 of 5 / Section 1.2 – 1.4

Now lets look at a description of the person's movement in each of the major sections.

Zero to 90s

Look at how you are running in those first 90 seconds.

● Every 30 seconds you have moved about another

150m away from the starting point… you must be

The slope of a d-t graph always equals

moving at a constant positive velocity!

the velocity of the object at that time.

● A constant positive velocity is shown on a d-t graph

as a straight line that slopes upwards. It is a linear

relationship.

● In fact, if you found the slope of the line in this section, it will be the velocity that you were running at.

rise d

slope=

= =v

run t

90s to 150s

Yikes! You ran too fast at the start and now you’re out of breath!

● During this time period, your position on the graph

has stayed the same…450m.

● This just means that you are standing in the same

spot, exactly 450m away from where you started.

● A flat horizontal line means you are stopped.

The slope of the line is the velocity, and

the slope of a flat line is zero. So, the

velocity is zero.

150s to 240s

You must have started running forward again, since a positively sloped line means a positive velocity. ● Notice that this section of line is a little steeper than the first section. You are now running about 200m every 30s.

● A steeper line (which has a bigger slope) means that you are moving at a faster constant velocity.

240s to 300s

In this section the line slopes down, which means it has a negative slope. ● Since slope is equal to velocity, this must mean that you are running backwards. ● A negative slope means a constant negative velocity.

● You must have forgotten to pass a check point, so you ran back to it.

300s to 360s

Again, we have a horizontal line. You must be stopped.

360s to 510s

You know that you have only one chance to still win the race… run as fast as you can! ● During this time period, the line curves upwards.

● The line becomes steeper and steeper as it continues. This means that the slope of the line is getting bigger and bigger.

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© studyphysics.ca

Page 2 of 5 / Section 1.2 – 1.4

●

●

Since slope is related to velocity, your velocity must be increasing. You are accelerating!

A curved line on a d-t graph means

A curved line on a d-t graph means

acceleration is happening.

acceleration.

Here’s how you can remember if it was positive or negative acceleration on a d-t graph.

d

d

t

t

Illustration 2: Happy

Clown

●

●

Illustration 3: Unhappy

Clown

If you see any part of the happy clown's face on a graph, it is positive acceleration. If you...

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