1. Motion and Motion Graphs

2. Kinematics Kinematics is the study of motion
Dynamics is the study of the causes of motion
Kinematics uses scalar and vector quantities to describe motion
Scalar quantities have only magnitude
Vector quantities have both magnitude and direction

3. Speed and Velocity The difference between speed and velocity:
Speed is a scalar quantity
Velocity is a vector quantity
Average speed is the total distance divided the total time
Average velocity is the displacement divided by the time interval for the change; the slope of a secant on a position-time graph

4. Average Velocity
To determine the average velocity of an object, we take the secant: the slope of a straight line connecting two separate points on a curve

5. Example
A jogger takes 25.1 s to run a total distance of 165 m by running 140 m [E], and then 25 m [W]. The displacement is 115 m [E].
Calculate the jogger’s average velocity
Calculate the jogger’s average speed

7. Instantaneous Velocity
To find the instantaneous velocity of a person or object from a graph, we must take the tangent at a specific time interval on the graph
A tangent is a straight line that intersects a curve at a point and has the same slope as the curve at the point of intersection

8. Average Velocity and Graphing
The position-time graph shows the detail of how an object is moved.
Calculate the average velocity during the time interval t1 = 1.0 s to t2 = 2.5 s.
Analyze the position-time graph. Use your analysis to sketch a qualitative velocity-time graph of the object’s motion

10. Examples
Analyze the graphs below. Create a corresponding velocity-time graph for each graph.

13. Acceleration
Average and instantaneous acceleration are calculated in the same manner as velocity
Average acceleration is the change in velocity divided by the time interval
Instantaneous acceleration is the acceleration at a particular instant in time

14. Creating Acceleration-Time Graphs
Suppose a sprinter is running a 100 m dash. The sprinter’s time and distance data have been recorded and used to make the velocity-time graph below.
Analyze the graph and make a sketch of an acceleration-time graph
From the acceleration-time graph, determine the maximum acceleration and the time at which it occurs

16. Classwork/Homework
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