Forces and Motion

5.1 – Use measurement & time-distance graphs to represent the motion of an object in terms of its

position, direction or speed.

Motion• Motion is a change in position of an object

with respect to time. • The following terms are used to describe

and measure motion.– Position– Direction– Speed

Position

• Position – the location of an object. Change in position is measured by distance (length of the path) moved from one position (reference point) to another.– What is a reference point?

Class demonstration: One volunteer and the rest of the class is split into two groups. This activity will illustrate the idea of a reference point.

Reference Point – is a place or object used for comparison to determine if something is in motion. An object is in motion if it changes position relative to a reference point.

Direction

• Direction – is the relationship of the position of a moving object to another position.

Speed

• Speed – is the rate of change in position or “rate of motion”. How long it takes to move from point A to B. – Speed does not necessarily mean that

something is moving fast.

Average Speed

• The average speed of an object tells you the (average) time at which it covers a given distance. – Average speed is the result of the total

distance divided by the total time taken.

Calculating Average Speed(v = d/t)

• v = d/t where:• v is the average speed of an object• d is the distance or length of the path of

the object• t is the time taken to cover the path

• Speed is measured using the following types of units:– meters per second (m/s)– kilometers per hour (km/h)– miles per hour (mph)

What is the difference between speed and velocity?

Velocity is speed with direction

V=d/t

v

d

t

d=vt t=d/v

TO HELP SOLVE EQUATIONS, HERE IS A STEP BY STEP GUIDE TO FOLLOW.

G U E S S

G – find your Givens

U – what is your Unknown (trying to find)

E – what is the Equation you need?

S – Substitute your givens

S - Solve

Examples:• Calculate the speed of an object using the

following information:t = 35 s and d = 50m

Step 1 – GUESSGivens are t = 35 s and d = 50 mUnknown: vEquation: v = d / tSubstitute: v = 50 / 35Solve: v = 50 divided by 35

Examples• Suppose a cyclist travels 32 kilometers during

the first two hours of riding, and 13 kilometers during the next hour. Calculate the average speed:

-total distance = 32km + 13km-total time = 2h + 1h

Average speed: 45km/3h = 15km/h or 15 kilometers per hour

Examples• Use the speed equation to determine how

far an object traveled. v=7m/st=3s

How far did the object travel?Rearrange v=d/t

d=vtd=7m/s(3s)d=21m

1.How long will it take to get to Atlanta, GA for a Falcons game from Greenville, SC (145 miles or 233 km). You know you can travel about 70 mph?

2. If a bamboo plant grows 28 centimeters in 11 days, what was the average speed the plant grew per day?

3. A soccer player was practicing on the soccer field last week. He ran back and forth on the field for a total of 750 yards. His average speed was 12 yards per second. How long did it take him to finish?

Graphing Speed

• Do you think it is possible to represent speed using a graph?

• If so, what type of graph would you use?– Line graph, bar graph, circle graph????

• When graphing speed you would use a line graph.

• A line graph shows the relationship between distance and time and how it relates to speed.

• The slope of the line gives us information about the speed and direction of an object.

• You graph speed by taking measurements of time and distance.

• For instance: The following measurements were taken on how fast a turtle walks along a path.

Time (h) Distance (m)0 01 52 103 154 155 156 107 5

Speed (m/h)

05

101520

1 2 3 4 5 6 7 8

Time (h)

Dis

tanc

e (m

)

Speed (m/s)

05

101520

1 2 3 4 5 6 7 8

Time (s)

Dis

tanc

e (m

)

At position A, is the object moving away from or towards the reference point?

At position C, is the object moving away from or towards the reference point?

A

B C

Steeper Slope = Faster Speed

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7

Time (s)

Dist

ance

(m)

Flatter Slope - Slower Speed

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 10 11 12 13

Time (s)

Dist

ance

(m)

Series2

The steeper the slope, the faster

the speed.

The flatter the slope, the slower

the speed.

Steeper Slope = Faster Speed

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7

Time (s)

Dist

ance

(m)

When the slope of the line is horizontal to the x-axis, the speed is zero (the object is not

moving)

Examples:

• Lets graph the motion of a drag racer.

Time (s) Distance (m)0 05 20

10 4015 6020 8030 10040 120

Have to allow for a

#25 and #35 on your X

axis!

First, we need to label the data x and y.

Time (s) Distance (m)0 05 20

10 4015 6020 8030 10040 120

X axis Y axis

Next, draw and label the graph.Speed

020406080

100120140

1 2 3 4 5 6 7

Time (s)

Dist

ance

(m)

Now, you need to plot the points.

Time (s)

Distance (m)

0 05 20

10 4015 6020 8030 10040 120

Practice Problem:• Graph the speed of

an object as it travels down hill.

Time (s) Distance (m)

0 01 22 53 94 155 20

Time (s) Distance (m)

0 01 102 83 54 35 1

Graph the speed of an object as it travels up hill.