Distance vs. Time

Analysis of a

Distance vs. Time Graph

What can the motion on a

Distance (d) vs. Time (t) Graph

Where did the object start?

Which direction did it go?

Where did the object stop?

Is the motion uniform (constant)?

Is the motion non-uniform (changing)?

Can you tell which is faster? (if 2 or more objects are

present)

Distance vs. Time Graph

Describing a journey made by an object is not exciting if

you just use words. As with much of science, graphs are

more revealing.

Plotting distance against time can tell you a lot about a

journey. Let's look a closer look:

Distance Time Graph

Time always runs horizontally (the x-axis).

The arrow shows the direction of time. The further to the

right, the longer time from the start.

Distance runs vertically (the y-axis).

The higher up the graph we go, the further we are from

the start.

The slope of a line on a distance-time graph is speed

The steeper the slope, the faster you are traveling

The flatter the slope, the slower you are traveling

Graphing Motion

Not moving? This is what it looks like…

If something is not moving, a horizontal line is drawn in a

distance-time graph

Time is increasing to the right, but its distance does not

change. It is stationary.

Moving….

If something is moving at a steady speed, it means we

expect the same increase in distance in a given time:

Time is increasing to the right, and distance is increasing steadily with time. It moves at a steady speed.

Can you describe what is going on here?

First part : Steady (slow) speed

Second part: Increase in speed (Covering a much larger distance in the same time.)

What are the three parts to the journey shown below:

Moving at a steady speed (slowly)

Not moving for quite some time

Moving again, but at higher speed

Example #1

Each line (A and B) represent the motion of two objects. Which object

is moving faster? Explain.

Graphing Motion

Example #2

Which car has a faster speed: The big car or small car? Explain

Graphing Motion

Example #3

Using this graph, what is the average speed of the Big Car

and the average speed of the small car?

Graphing Motion

Different Motion Graph Examples

What is the slope of a distance vs. time graph?

Speed!!!

What is the speed of the airplane?

Phoenix

Denver

Rise=?

3 hours

600 m

Speed = Slope = Rise/

Rise/

What is the speed of the airplane?

Different Slopes

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7

Time (hr)

Dis

tan

ce (

km

)

Run = 1 hr

Run = 1 hr

Run = 1 hr

Rise = 0 km

Rise = 2 km

Rise = 1 km

Slope = Rise/Run

= 1 km/1 hr

= 1 km/hr

Slope = Rise/Run

= 0 km/1 hr

= 0 km/hr

Slope = Rise/Run

= 2 km/1 hr

= 2 km/hr

Question

• Below is a distance vs. time graph of my position

during a race. What was my AVERAGE speed for

the entire race?

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6

Time (hr)

Dis

tan

ce (k

m)

Average Speed = Total distance/Total time = 12 km/6 hr

= 2 km/hr

Run = 6 hr

Rise = 12 km

Question

Below is a distance vs. time graph for 3 runners. Who

is the fastest?

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 35

Time (h)

Dis

tan

ce (

mi.)

Bob

Jane

Leroy

Leroy is the fastest. He completed the race in 3 hours

Here is another time-distance graph with 2 journeys represented on the same graph.

Each line represents a journey from home to the office.

The red line is Dave’s journey.

The green line is Mike’s journey.

1000 m

500 m

0 5 10 15

D

i

s

t

a

n

c

e

Time (min)

How long after Dave does Mike

leave?

3 min

After how many minutes does

Mike catch up?

7 min

How far from home are they

then?

Dave: 71.66 m/min

Mike: 100 m/min

What is the speed of each

person?

500 m

1500 m

Question #4

What is going on in each section of the following distance-time

graph?

3.5 Assessment Questions

3.5 Homework

• Graphing “Little Dudes I”

• Graphing “Little Dudes II”

• Little Dots in Uniform Motion