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.

Measurements  A 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 10 9 s.  One beat of mosquito wing = 5 x 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.  Looking for:  …the time in seconds  Given:  …time in mixed units  Relationships:  1 min. = 60 sec.; 1 hr. = 3600 sec.  Solution:  Convert min. to sec, convert hr. to sec, then add all the seconds together. Solving Problems

 Solution:  30 min. x 60 sec. = 1800 sec. 1 min.  2 hr. x 3600 sec. = 7200 sec. 1 hr.  1800 sec sec sec 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  Decide which variable to put on the x-axis and which to put on the y-axis.

How to make an XY graph  Make a scale for each axis by counting boxes to fit your largest value for each axis.

How to make an XY graph  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.  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  Draw a smooth curve that shows the pattern of the points.  Create a title for your graph.