From last time. Light and heavy objects fall identically. Objects maintain their state of motion unless acted on by an external force.

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1 From last time Light and heavy objects fall identically. Objects maintain their state of motion unless acted on by an external force. I.e. either at rest, or straight line motion at constant speed This means that a falling body is acted on by a force gravity. HW#1 assigned (see web page)

2 Position, speed, velocity, & acceleration Today we talk about details of the motion We introduce important concepts: position distance speed, velocity average instantaneous acceleration average instantaneous

3 A moving object changes its position with time. x 1 = pos. at time t 1 x 2 = pos. at time t 2 Quantifying motion: Distance and Time x 1, t 1 x 2, t 2 e.g. at 10:00 am, I am 3 meters along the path (x 1 =3 m, t 1 =10:00 am) at 10:00:05 am, I am 8 meters along the path (x 2 =8 m, t 1 =10:00:05 am) My position at all times completely describes my motion

4 Can use this information to find the speed If I move 5 meters in 5 seconds. Then # meters in each second = 5 divided by 5 = 1 meter per second. e.g. could walk 1 meter in the first second, and 1 meter in the next second, etc. BUT maybe I walked 0 meters in the first second and then 5 meters in 4 seconds.

5 The average speed is the same Average speed = distance traveled traveling time As an equation: Distance traveled = d Traveling time = t Average speed = s s = d t Could also write d = s t So knowing average speed lets us find distance traveled

6 Instantaneous speed Instantaneous speed is the average velocity over an infinitesimal (very short) time interval. This is what your speedometer reads. Instantaneous speed gives you a better understanding of the motion.

7 Think about this one: The instantaneous speed is A. Always less than the average speed B. Always greater than the average speed. C. Sometimes less than and sometimes greater than the average speed.

8 Units All of these quantities have units Distance: measured in meters, miles, feet Time: measured in seconds, hours, years Speed: meters per second, miles per hour In this course we will generally use the mks system of units Length meter (m) Mass kilogram (kg) Time second (s) Derived units Speed: meters per second (m/s), miles per hour (mph)

9 Speed and Velocity Walking 3 meters north in 2 seconds is different than walking 3 meters south in 2 seconds. Speed is the same, but end location is different. This arises so frequently we define a new word: Velocity means speed and direction

10 Average velocity: Average Velocity displacement divided by the time of travel has the same direction as displacement v = Δx Δt = x 2 x 1 t 2 t 1 Velocity has a direction e.g. can be positive or negative

11 Acceleration Acceleration is the rate at which velocity changes: Acceleration = change in velocity time to make the change

12 Understanding acceleration Constant velocity Zero acceleration Increasing velocity Constant acceleration in the same direction as v Decreasing velocity Constant acceleration opposite of v

13 Back to Galileo Use position, velocity, acceleration to quantify the motion of a falling object.

14 Distance vs time for falling ball From analyzing the video frame by frame we find the position vs time. Clearly position is not proportional to time Not constant velocity DISTANCE ( meters ) Falling Ball TIME ( seconds )

15 Average speed for falling ball Total time=0.73s Total distance=2.6m Avg speed = 0.73s/2.6m=3.6 m/s DISTANCE ( meters ) Falling Ball TIME ( seconds )

16 Distance vs time for falling ball speed = speed = speed = 2.6m 2.0m 0.73s 0.638s 1.2m 0.8m 0.488s 0.40s 0.4m 0.2m 0.275s 0.18s = 6.5m /s = 4.5m /s = 2.1m /s DISTANCE ( meters ) Falling Ball TIME ( seconds ) 0.22s 0.45s 0.69s

17 Speed vs time Instantaneous speed increases proportionally to time s=at VELOCITY ( m/s) TIME ( s )

18 Fit to t 2 law d = 1 2 at 2 a=9.83 m/s 2 DISTANCE ( meters ) m1 Chisq R Falling Ball y = 0.5*m1 * M0^2 Value Error NA NA TIME ( seconds )

19 Converting units A major league pitcher can throw the ball 100 miles per hour. What is the ball speed in m/s? (5 miles is approximately 8 km) m/s m/s ms correct 100 miles hour 8 km 5 miles 1000 m 1 km 1 hour 3600 s = m /s

20 Making estimates Order of magnitude estimate: A mile is of order 10 3 meters An hour is of order 10 3 seconds Then the answer should be of order 10 2 m/s

Distance vs. Displacement, Speed vs. Velocity, Acceleration, Free-fall, Average vs. Instantaneous quantities, Motion diagrams, Motion graphs,

Distance vs. Displacement, Speed vs. Velocity, Acceleration, Free-fall, Average vs. Instantaneous quantities, Motion diagrams, Motion graphs, Kinematic formulas. A Distance Tells how far an object is from