Car and Ramp

Part One: Distance and Time

Learning Goals

Accurately measure distance. Identify metric and English units of distance.

Convert between units of distance.

Calculate speed in units of inches per second, feet per second, and centimeters per second.

MeasurementsA measurement is a determination of the amount of something.

A measurement has two parts: a number value

and a unit

Distance

Distance is the amount of space between two points.

Distance is measured in units of length.

The meter is a basic SI distance unit.

In 1791, a meter was defined as one ten-millionth of the distance from the North Pole to the equator. What standard is used today?

Two common systems

The English System is used for everyday measurements in the United States.

Miles, yards, feet, inches, pounds, pints, quarts, gallons, cups, and teaspoons are all English system units.

In 1960, the Metric System was revised and simplified, and a new name was adopted—International System of Units.

International System of Measurement (SI)

The acronym SI comes from the French name Le Système International d’Unités.

SI units form a base-10 or decimal system.

In the metric system, there are: 10 millimeters in a centimeter, 100 centimeters in a meter, and 1,000 meters in a kilometer.

Metric prefixes

Prefixes are added to the names of basic SI units such as meter, liter and gram.

Prefixes describe very small or large measurements.

Time and Distance

Two ways to think about time:

What time is it?

How much time?

A quantity of time is also called a time interval.

Time Relationships

Time scales in physics

The second (s. or sec.) is the basic unit of time in both the English and metric systems.

Things in the universe happen over a huge range of time intervals.

Average life span of human = 2.2 x 109 s.

One beat of mosquito wing = 5 x 10-4 s.

Time Relationships

A microwave oven can understand time in either mixed units (minutes and seconds) or in a single unit (seconds).

Both 1:30 and 0:90 will result in the same cooking time.

Converting Units

For calculations, you may need to convert hours and minutes into seconds.

How many seconds is this time interval?

Convert 2 hr, 30 min and 45 sec.1. Looking for: …the time in seconds

2. Given: …time in mixed units

3. Relationships: 1 min. = 60 sec.; 1 hr. = 3600 sec.

4. Solution: Convert min. to sec, convert hr. to sec,

then add all the seconds together.

Solving Problems

Solving Problems

4. Solution: 30 min. x 60 sec. = 1800 sec.

1 min. 2 hr. x 3600 sec. = 7200 sec.

1 hr. 1800 sec.

7200 sec.+ 45 sec.

9045 sec Answer 9045 sec.

Graphing A graph is a picture that shows

how two variables are related.

A scatterplot or XY graph is used to see if two variables are related.

Graphs show relationships

By convention, or common agreement, graphs are drawn with the independent variable on the horizontal or x-axis.

We say time is the independent variable in a position-time graph because the time interval was decided before the experiment.

Graphs show relationships

The dependent variable goes on the vertical or y-axis.

Position in a position-time graph is the dependent variable because the car’s position will depend on time.

How to make an XY graph

1. Decide which variable to put on the x-axis and which to put on the y-axis.

How to make an XY graph

2. Make a scale for each axis by counting boxes to fit your largest value for each axis.

How to make an XY graph

3. Count by multiples of 1, 2, 5, 10, or a larger number if needed. Write the numbers on each axis at evenly spaced intervals and label each axis with its corresponding variable and unit.

4. Plot each point by finding the x-value and tracing the graph upward until you get to the right y-value. Draw a dot for each point.

How to make an XY graph

5. Draw a smooth curve that shows the pattern of the points.

6. Create a title for your graph.