Chapter 3 Linear Motion

5.DESCRIPTION OF MOTION Speed Velocity Acceleration

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

Distance vs. Time graph Time Distance Instantaneous Speed is the slope of this graph at a point

Average Velocity Time Distance  Find end-points  Connect with a line  Find slope of the line

Choose Different End-Points Time Distance  Find end-points  Connect with a line  Find slope of the line

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

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 Acceleration = "change" in velocity/time Units - m/s 2, ft/s 2, etc. Acceleration is also a vector Velocity Time Acceleration is the slope of a Velocity vs. Time graph.

Motion at constant velocity Accelerated motion HereHere, too

Demo - Ball on incline and ball on table Deceleration = negative acceleration

Acceleration on Galileo's Inclined Planes (equal time slices)

Velocity and Acceleration Galileo used inclined planes to study accelerations. He found constant accelerations for inclines. (It was too hard to measure time for free-falls.) He also found that the mass 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?

6.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

How Fast Velocity in gravitational field (starting from rest) v = gt = 32t English Or v = 10t Metric

Distance Equation d o = initial distance v o = initial velocity g = acceleration due to gravity

Free Fall Falling in a gravitational field: Take d o and v o to be zero (object starts from the origin at rest) Then: d = d o + v o t + ½at 2 becomes d = ½gt 2 d = 5t 2 (Metric)

Free Fall Time of Fall (s) Velocity Acquired (m/s) – 10t Distance Fallen (m) – 5t

Demonstrations Demo - Reaction timer Demo - Paper and book drop

Free Fall Graphs Ball released from rest, down positive, measure distance from point of release.

Different Assumptions Ball thrown up from origin with an initial speed of 10 m/s, up is positive

Free Fall - How Quickly How Fast Acceleration Is How Quickly - How Fast - Changes in Velocity Acceleration is difficult to understand because it is a rate of a rate.