Representing Motion

Chapter 2

Physics Principles and Problems

Zitzewitz, Elliot, Haase, Harper, Herzog, Nelson, Nelson, Schuler

and Zorn

McGraw Hill, 2005

Motion• An object whose position changes over time.• Motion Diagram - shows the positions of a

moving object at successive times.

http://www.sunfairrun.com/t&f_2006/trackphotos/5-19regionals/reg1.jpg

Visualizing Motion• Coordinate System - shows the location of the zero

point (origin) and direction of an object in motion.

• Arrows can be utilized to show an objects position and distance traveled.

http://www.cs.utexas.edu/~okan/papers/s2003/pictures/fig5.jpg

Vectors and Scalars

• Vectors are quantities that have both magnitude (size) and direction.

0 15m

• Scalars are quantities that are numbers without direction

4C, 5m, 39s, 22m/s

Resultant Vectors

• Vector that represents the sum of two or more vectors.

• Based upon their direction some vectors can be negative.

http://media.nasaexplores.com/lessons/04-029/images/sum.gif

Time Intervals and Displacement

• Time Interval - equals the final time (tf) minus the initial time (ti)

∆ t = tf - ti

• Displacement - equals the final position (df) minus the initial position (di)

∆ d = df - di

Position - Time Graphs• By plotting the time (t) and position (d) data of a

particular object a position-time graph can be generated.

• Remember that d represents that object’s instantaneous position.

http://dev.physicslab.org/img/17b988eb-9b4c-47ee-adab-0e66059c0ba7.gif

t d5 3010 6015 6020 4025 2030 035 -2040 -4045 -3050 -1055 0

Average Velocity• Defined as the change in position divided by

the time during which the change occurred.

v = ∆d / ∆t = df - di / tf - ti

• Average velocity is represented by the slope of the line in a position-time graph

http://dev.physicslab.org/img/17b988eb-9b4c-47ee-adab-0e66059c0ba7

Speed vs. Velocity• Speed is how fast an object in moving. It is a scalar

quantity and therefore can never be negative.• Velocity is speed with direction. It is a vector quantity

and therefore can be negative.• Instantaneous velocity is the speed and direction of an

object at a particular instant.

http://hadithuna.com/files/2008/04/d737speed-racer-go-speed-posters.jpghttp://www.jimcarroll.com/weblog/archives/pictures/velocity.jpg

Equation of Motion for Average Velocity

• An object’s position is equal to the average velocity multiplied by time plus the initial position.

d = vt + di

• Use algebra and the equation v = d / t to solve for any of the variables.