Understanding Motion: Key Concepts of Distance, Displacement, Speed, and Velocity

Constant Motion

Reference Point A fixed point from which direction is defined. The reference point can be anything.

Distance The length traveled along a trip measured from start to finish.

Example #1 A car drives 4 meters north, 3 meters south then 5 meters north. What’s its total distance driven? 4m + 3m + 5m = Total distance driven 12m

Direction Represented by the using : (+) or (-) signs Up or Down Right or Left Forward or Backward North, South , East or West

Position The location of an object, relative to the reference point.

Displacement The difference between two positions. Dd = dfinal – dinitial

Example #2 A car drives 4 meters north, 3 meters south then 5 meters north. What’s its displacement?

Time Interval The difference between two clock readings t = tfinal – tinitial

Average Speed Total distance traveled divided by the total time elapsed. v = d / t

Average Velocity Total displacement divided by the total time elapsed. v = Dd / Dt

Average Acceleration Average velocity divided by the time. a = v / t

Example #3 While Ned is traveling along a straight interstate highway, he notices that the kilometer marker reads 260. Ned reaches the 150-kilometer marker 45 minutes later then retraces his path for one hour before arriving at the 225-kilometer marker. Use the GUESS Method Skills Sheet

Example #3A How far (distance) did Ned travel? G: dinitial = 260 km dfinal = 150 km t = 45 minutes dinitial = 150 km dfinal = 225 km t = 1 hour U: distance Answer: 185 km

Example #3B What’s Ned’s total displacement? G: dinitial = 260 km dfinal = 150 km dinitial = 150 km dfinal = 225 km U: displacement ANSWER: 35 km

Example #3C What’s Ned’s average speed in meters per second? G: d = 185 km → 185 x 103m t = 1 hour 45 minutes → 6300 s U: average speed E: v = d/t S: v = (185 x 103 m )/ (6300s) S: v = 29.365 m/s

Example #3D What’s Ned’s average velocity in meters per second? G: d = 35 km → 35 x 103 m t = 6300 s U: average velocity E: v = Dd/Dt S: v = (35 x 103 m)/ 6300 s S: v = 5.556 m/s

Example #4 • What is the time required to make a 300 km trip if the average speed is 29 m/s? Show your answer in base units and correct scientific notation form. G: d = 300 km → 300 x 103 m v = 29 m/s U: t E: v = d/t → t = d/v S: t = (300 x 103 m)/ 29 m/s S: t = 1.0345 e 4 s

Example #5 • A dolphin swims 1.85 km/h. How far has the dolphin traveled after 0.60 h? Show your answer in base units and correct scientific notation form. G: v = 1.85 km/h → 1.85 x 103 m / 3600 s t = 0.6 h → 2160 s U: d E: v = d / t → tv = d S: d = (5.139 x 10-1 m/s)( 2160 s ) S: v = 1.11e 3 m

Example #6 A sailboat moves at a constant speed of 2 m/s. How far does it travel every ten seconds? Show your answer in base units and correct scientific notation form. G: v = 2 m/s t = 10 s U: d E: v = d/t → d = tv S: d = (10 s)(2 m/s) S: d = 20 m

Example #7 A truck is traveling at a constant velocity of 70 km/h. Convert the velocity to m/s. G: v = 70 km / h U: v in (m / s) E: simple conversion S: ( 70 x 103 m ) / 3600 s S: 1.944 e 1 m/s

Understanding Motion: Key Concepts of Distance, Displacement, Speed, and Velocity