Chapter 3 Linear Motion

1.MOTION IS RELATIVE Everything moves, at least with respect to some reference point. To describe motion we shall talk about Speed Velocity Acceleration

= distance/time Units - m/s, ft/s, etc. Instantaneous Speed is the speed you would read from a speedometer. 2.Speed Average Speed

Example of Average Speed  You take a trip from A to B and back to A.  You want to average 60 mph for the round trip A to B to A. A B 2 miles From A to B you average 30 mph. What is your average speed on the return trip from B to A? 30 mph ?

Example of Average Speed A B 2 miles 30 mph ?  60 mi/hr is 60 mi/(60 min) or 1 mi/min.  To average 1 mi/min for a 4 mi trip would require 4 min.  30 mi/hr is 30 mi/(60 min) or 1 mi/(2 min).  A 2 mi trip would take 4 min.  See a problem???

Sorry, Ma’am, but you were doing 45 mph in a 30 mph zone. But I haven’t driven 45 miles yet. Speeding Little Old Lady Okay, okay, would you believe that I haven’t been driving for an hour yet?

3.Velocity  Average Velocity = Displacement/time  Units - m/s, ft/s, etc.  Instantaneous Velocity of an object is its instantaneous speed plus the direction it is traveling.  Velocity is a vector.

Displacement and Average Velocity Distance traveled is the length of the path taken. Average velocity =

Acceleration = "change" in velocity/time Units – (m/s 2 ), 4.Acceleration (ft/s 2 ), etc. Acceleration is also a vector.

Motion at constant velocity Accelerated motion Here Here, too

 Demo - Ball on incline and ball on table  We can sense acceleration by comparing observations from a constant velocity frame of reference to observations from an accelerating frame of reference.  Interpretation - we can feel acceleration if there is a “support” force or contact.

Acceleration on Galileo's Inclined Planes

Velocity and Acceleration  Galileo used inclined planes to study accelerations.  He found constant accelerations for inclines: the steeper the incline, the greater the acceleration. (It was too hard to measure time for free-falls.)  He also found that the size of the objects didn't matter.

Relationships Between v and a for Linear Motion. If initial velocity is zero, then

Example A jogger starts at zero velocity with an acceleration of 3 ft/s 2. How fast is she moving after 4 seconds? (Let’s see if we can first do this without using any equations.)

Chapter 3 Review Questions

What is the average speed of a horse that gallops a round-trip distance of 15 km in a time of 30 min? (a) 0 (b) 0.5 km/h (c) 30 km/h (d) 500 m/s (e) None of the above

What is the average velocity for the round-trip of the horse in the previous question? (a) 0 (b) 0.5 km/h (c) 30 km/h (d) 500 m/s (e) None of the above

5.FREE FALL Motion near the surface of the earth in the absence of air resistance. The acceleration of an object is g = 32 ft/s 2 = 9.8 m/s 2.

Velocity in gravitational field: v = gt = 32t How Fast

How Far BC and how deep is a well. Michael Jordan – 3 s hang time?? (If initial velocity is zero)

Free Fall Time of Fall (s) Velocity Acquired (ft/s) Distance Fallen (ft)

Demonstrations  Demo - Coin and feather in vacuum  Film - Galileo's Experiment on the Moon  Demo - Reaction timer  Demo - Paper and book drop

What is the acceleration of an object at top of its flight? g, you should know this one.

Free Fall - How Quickly How Fast Changes  Acceleration Is How Quickly How Fast Changes.  Acceleration is difficult to understand because it is a rate of a rate.  What is a rate of a rate of a rate? JERK

Chapter 3 Review Question

You throw a stone downward. It leaves your hand with a speed of 10 ft/s. What is its speed two seconds after leaving your hand? (Neglect air resistance.) (a) 10 ft/s (b) 32 ft/s (c) 42 ft/s (d) 64 ft/s (e) 74 ft/s

An object dropped from rest in free fall will fall feet in the first second and feet in the second second. (a) 16, 48 (b) 16, 32 (c) 32, 32 (d) 32, 64 (e) 32, 48