Definition of Speed Speed is the distance traveled per unit of time (a scalar quantity).Speed is the distance traveled per unit of time (a scalar quantity). v = = stst 20 m 4 s v = 5 m/s Not direction dependent! A B s = 20 m Time t = 4 s

Definition of Velocity Velocity is the displacement per unit of time. (A vector quantity.)Velocity is the displacement per unit of time. (A vector quantity.) v = 3 m/s at 20 0 N of E Direction required! A B s = 20 m Time t = 4 s D=12 m 20 o

Average Velocity and Instantaneous Velocity The instantaneous velocity is the magn- itude and direction of the speed at a par- ticular instant. (v at point C)  The average velocity depends ONLY on the displacement traveled and the time required. A Bs = 20 m Time t = 4 s C

Average and Instantaneous v xx tttt x2x2x2x2 x1x1x1x1 t2t2t2t2 t1t1t1t1 xx tt Time slope Displacement, x Average Velocity: Instantaneous Velocity:

Example 1. A runner runs 200 m, east, then changes direction and runs 300 m, west. If the entire trip takes 60 s, what is the average speed and what is the average velocity? Recall that average speed is a function only of total distance and total time: Total distance: s = 200 m m = 500 m Avg. speed 8.33 m/s Direction does not matter! start s 1 = 200 m s 2 = 300 m

Example 1 (Cont.) Now we find the average velocity, which is the net displacement divided by time. In this case, the direction matters. x o = 0 t = 60 s x 1 = +200 m x f = -100 m x 0 = 0 m; x f = -100 m Direction of final displacement is to the left as shown. Average velocity: Note: Average velocity is directed to the west.

Example 2. A sky diver jumps and falls for 600 m in 14 s. After chute opens, he falls another 400 m in 150 s. What is average speed for entire fall? 625 m 356 m 14 s 142 s A B Average speed is a function only of total distance traveled and the total time required. Total distance/ total time:

Relative Velocity How fast? It all depends on who you ask!! How fast? It all depends on who you ask!!

Relative Velocity Velocity is a vector quantityVelocity is a vector quantity How it is measured depends on the frame of referenceHow it is measured depends on the frame of reference The same motion can be described differently, based on the frame of referenceThe same motion can be described differently, based on the frame of reference

Frame of Reference When making measurements of the physical world, a reference point and directional system must be chosenWhen making measurements of the physical world, a reference point and directional system must be chosen All measurements are made from this reference point and within this directional systemAll measurements are made from this reference point and within this directional system This frame of reference does not always have to be stationary…This frame of reference does not always have to be stationary…

Motions Observed from Different Frames of Reference

Relative Velocity Velocity of A relative to B: V AB =V A -V B V AB =V A -V B v AB : v of A with respect to B v B : v of B with respect to a reference frame (ex.: the ground) v A : v of A with respect to a reference frame (ex.: the ground)

Example 1 The white speed boat has a velocity of 30km/h,N, and the yellow boat a velocity of 25km/h, N, both with respect to the ground. What is the relative velocity of the white boat with respect to the yellow boat?The white speed boat has a velocity of 30km/h,N, and the yellow boat a velocity of 25km/h, N, both with respect to the ground. What is the relative velocity of the white boat with respect to the yellow boat? Answer: 5km/h, NAnswer: 5km/h, N

Example 2- The Bus Ride A passenger is seated on a bus that is traveling with a velocity of 5 m/s, North. If the passenger remains in her seat, what is her velocity: a)with respect to the ground? b)with respect to the bus?

Relative Velocity in 2D Constant velocity in each of two dimensions (example: boat & river, plane and wind) Velocity of Boat in Still Water Velocity of River with respect to the ground

Adding vectors that are at 90 0 to each other. Draw the vector diagram and draw the resultant. Use the Pythagorean Theorem to calculate the resultant. Use θ=tan -1 (y/x) to find the angle between the horizontal and the resultant, to give the direction of the resultant. (0 0 is along the +x axis)

Example 4-Airplane and Wind An airplane is traveling with a velocity of 50 m/s, E with respect to the wind. The wind is blowing with a velocity of 10 m/s, S. Find the resultant velocity of the plane with respect to the ground. Answer: 51m/s, at 11 o S of E.

Independence of Vector Quantities Perpendicular vector quantities are independent of one another.

Independence of Vector Quantites Example: The constant velocities in each of the two dimensions of the boat & river problem, are independent of each other. Velocity of Boat in Still Water Velocity of River with respect to the ground

Example 5- Boat and River A boat has a velocity of 4 m/s, E, in still water. It is in a river of width 150m, that has a water velocity of 3 m/s, N. a) What is the resultant velocity of the boat relative to the shore. b) How far downstream did the boat travel? Answer: a) 37 o above + x axis (E) b) 113m

CONCLUSION OF Chapter 6 - Acceleration