Foundations of Physical Science Unit 1: Forces and Motion

Chapter 2: Mathematical Models 2.1 Using a Scientific Model to Predict Speed 2.2 Position and Time 2.3 Acceleration

Learning Goals Construct a speed vs. distance graph. Use a graph to make a prediction that can be quantitatively tested. Calculate the percent error between a measurement and a prediction. Create and analyze a distance vs. time graph.

Learning Goals (continued) Determine the slope of a line. Distinguish between linear and nonlinear graphs. Distinguish between speed and acceleration. Calculate acceleration from a formula. Calculate acceleration from the slope of a speed vs. time graph.

Vocabulary accelerate acceleration average speed conceptual model deceleration dependent variable free fall graphical model gravity independent variable physical model scientific model

2.1 Using a Scientific Model to Predict Speed

Can you predict the speed of the car at any point on the ramp?

Scientific Models A model that shows how each variable from an experiment relates to another Mental models Physical models Conceptual models Graphical models

Making a Graphical Model A graph shows a relationship between the variable on the x-axis and on the y-axis Graphs use numbers and are considered “mathematical models” Dependent variable (y-axis) Independent variable (x-axis)

Making a Graphical Model Decide what to put on the x and y axis. Make a scale for each axis by counting boxes to fit your largest value. Plot your points by finding the x value, and drawing a line up until you get to the right y value. Put a dot for each point.

Making a Graphical Model Draw a smooth curve that shows the pattern of the points. Don’t simply connect the dots. Make a title for your graph.

Reading a Graph Graphs organize your data into a model you can use to make predictions

Cause and Effect Relationships How does one variable effect another? Graphs are a good way to see whether there is a connection or not

Cause and Effect Relationships Strong Weak Inverse

2.2 Position and Time

Position Position (Displacement)- comparison from starting point, includes direction Distance- interval of length without regard to direction Position and Distance-not the same thing!

Determining Speed from the Slope of a Graph Slope is the ratio of “rise” (vertical change) to the “run” (horizontal change) of a line. The rise is determined by finding the height of the triangle shown. The run is determined by finding the length along the base of the triangle

Speed The slope of the position vs. time graph

Instantaneous and Average Speed Does your speed stay exactly the same during a real trip? Average Speed: total distance divided by the total time taken (Initial velocity + Final velocity) 2 Instantaneous Speed: the speed you have at a specific point in your journey; use a position vs. time graph

2.3 Acceleration

Acceleration The rate at which velocity/speed changes with time Change: magnitude, direction or both a = change of velocity/time interval

Force Causes Acceleration To accelerate an object, it has to be pushed or pulled…a force is applied Force can be: Sudden Steady (i.e. gravity)

Acceleration a = (Vf - Vi)/t Vf = Final Velocity Vi = Initial Velocity t = time

Acceleration Slope of the speed-time graph = acceleration > slope = > acceleration

Deceleration (Negative Acceleration) < slope = < acceleration

No Acceleration (Constant Velocity) Zero acceleration = straight line on the speed-time graph constant speed = no acceleration

Acceleration

The Units of Acceleration Usually done in metric units Change in speed divided by change in time 5 Meters per second per second (m/s/s) 5 Meters per second squared (m/s2) The speed is increasing by 5 m/s every second

Free Fall A state of fall under the influence of only gravity Free from air resistance

Free Fall The amount of acceleration is the same for all freely falling objects in the same vicinity Freely falling objects gain speed at the rate of 9.8 m/s each second (9.8 m/s2)