1. One-Dimensional Motion

2. Experience vs. Experiment Through evolution and memory, humans have developed a “sense” for motion  Developed over years of observation, pattern recognition  This understanding is qualitative (“general”, “vague”)  No physics knowledge is required to catch a ball! In physics, we aim to understand motion through experiment  Measure location of objects at specific times  This understanding is quantitative (“specific”, “numerical”)  With physics, if you know how the ball will be thrown, you can predict where to stand to catch it!

3. Experience vs. Experiment – An Example Identical balls race down two tracks Which one will win the race? Experience:  Balls experience the same drop in height between starting point and end point, so the race should be a tie Experiment:  Measure position of each ball every second  Ball rolling on lowered track wins race!

4. Measurement of Motion: A Closer Look Question: “Where is the pen?”  Answer: “3 meters” (From where? In what direction?) To measure a position in space, we must start with a reference point  Sometimes called the “origin” of a reference frame  Position is relative; there is no universal origin Motion is also relative  Think of sitting in a train watching another train through the window – tough to tell which is moving  There is no universal “standing still”

5. Relative Motion Examples The Earth  Seems to be stationary in our experience  Astronomy: Earth actually moves at about 60,000 mph in orbit around the Sun  Sun moves at about 500,000 mph in orbit around the center of the Milky Way Galaxy  Our experience misleads us once again! Your car on the freeway  Moving at 65 mph relative to road surface  Moving at 5 mph relative to a car passing you  Moving at 130 mph relative to a car driving on the other side of the freeway

6. Speed Speed measures how quickly an object moves  Units: Examples:, mph  Instantaneous Speed: How fast an object is moving at a particular instant in time  Average Speed: How fast an object moves, on average, during a period of time Equation:  An instantaneous speed can be thought of as an average speed for an infinitely short trip

7. Average Speed vs. Instantaneous Speed: An Example The 100-meter dash  The best in the world run the race in about 10 seconds There are many instantaneous speeds during the race  Are any of them larger than the average speed?  Yes! The sprinter gets up to about 25 mph v t 10 sec 5 sec v average v instantaneous

8. Velocity Velocity is defined as speed and direction  50 meters / sec is a speed  50 meters / sec to the east is a velocity It is possible to change an object's velocity without changing its speed  Can you think of an example?

9. Acceleration Acceleration is the rate of change of velocity (not speed!)  Ways to accelerate your car:  Step on gas pedal (positive acceleration)  Step on brake pedal (negative acceleration)  Turn steering wheel (sideways acceleration) Equation :  Units: Example:

10. Acceleration: Why is it useful? Recall the work of Galileo and Newton  The “natural state” of an object is constant velocity By exerting forces on a system, we can change its state of motion  Forces change the system's velocity, causing acceleration

11. One-Dimensional Motion What is it?  Motion along a single line ( no turns or curves allowed )  Can move forward and/or backward along line  Only need one number to measure position Why is it important?  Once we understand 1-D motion, we can apply the same principles and equations to 2-D and 3-D motion Examples: Car on straight road Free fall Mass on spring

12. 1-D Motion Experiment: Galileo's “Inclined Planes” Observation: Ball gains speed as it rolls down incline Hypothesis: The acceleration of the ball is constant for a given incline Experimental Results: The ball's motion is consistent with constant acceleration

13. Galileo's Planes: Interpreting the Results By measuring the distance traveled during each second, we can figure out the average speed during each second  If acceleration is constant, the average speeds will fit a pattern v t 1 sec2 sec3 sec V average (during 1st second) V average (during 2nd second) V average (during 3rd second)

14. Free Fall If the only force acting on a physical system is gravity, the system is said to be in “free fall”  Let's ignore air resistance (for now) Measurements show that objects in free fall accelerate at about 10 m/sec 2  Regardless of their mass! In physics, we use this so commonly that we give it a name: F gravity

15. Free Fall Experiment Our experience tells us that heavy objects tend to fall faster than light objects  This is due to air resistance! We can remove air resistance by dropping objects in a vacuum  Voila! Objects accelerate at same rate

16. Free Fall – Equations Speed of free-falling object dropped from rest Distance fallen by free-falling object