Kinematics Speed & Velocity 7/7/2016TEKS 4A

Speed  Speed is the distance traveled per unit of time (a scalar quantity). v = = dtdt 20 m 4 s v = 5 m/s Not direction dependent! Speed = d distance (in meters) t time (in seconds) A B x = 20 m Time t = 4 s

Constant vs Changing Speed Constant speed refers to keeping the same speed throughout the entire distance traveled. Very few things stay at a constant speed. Did the car move at a constant speed?

On graphs that show distance and time, the SLOPE of the line is a measure of the speed of an object. Pick two points (X-value, Y-value) that are on the line. The easiest points to pick are points where the line crosses the grid of the graph paper. In this example, Point 1 could be ( 2, 400) Point 2 could be (4, 800) Plug these two points into the following formula to calculate the slope: Slope = Y 2 - Y 1 X 2 - X 1 Slope = Slope = 400 = Speed = 200 m/min

A car travels a distance of 500 m in 10 sec. What is the car's speed? s = d/t 50 m/s A second car travels a distance of 100 meters in 20 seconds. What is this car's speed? 5 m/s

Velocity 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 x= 12 m 20 o

Average Velocity Average velocity – the total displacement divided by the time interval which the displacement occurred. Velocity includes distance and direction. 7/7/2016 TEKS 4A

Average Velocity Formula average velocity = change in position change in time average velocity = displacement time interval v avg = Δx = x f - x i Δt t f - t i Key: Average velocity = v avg (m/s) Displacement = Δx (m) Final position = x f (m) Initial position = x i (m) Change in time = Δt (s) Final time = t f (s) Initial time = t i (s)

Example 1 During a race on level ground, Andrea runs with an average velocity of 6.02 m/s to the east. What distance does Andrea cover in 137 s? Step 1: Given v avg = 6.02 m/s d = ? t = 137 s 7/7/2016 TEKS 4A

Step 2: Formula Step 3: Substitute and Solve Δx = (6.02 m/s)(137s) Answer: Andrea’s distance is 825 m to the east. 7/7/2016 v avg = Δx Δt Δx = v avg Δt Manipulated formula 825m to the east

Velocity vs. Speed Not the same thing! Velocity describes motion with both direction and a numerical value (a/k/a magnitude ). Speed has no direction, only magnitude. 7/7/2016 TEKS 4A

What is Velocity? Velocity is a measure of the speed of an object AND the direction it is moving in space. On the escalator, passengers are moving at the same constant speed, but they are moving in different directions. Velocity can change even if speed is remaining constant (you just change direction)

Example – Velocity – A racecar on an oval track A racecar has a constant speed of 100 km/h and is going around an oval track. Even though the speed remains constant, the velocity changes because the direction of the car’s motion is changing constantly. 7/7/2016 TEKS 4A

Example 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? Total distance= 200 m m = 500 m Avg. speed 8.33 m/s Direction does not matter! start x 1 = 200 mx 2 = 300 m

Example (Cont.) Now we find the average velocity, which is the net displacement divided by time. In this case, the direction matters. x i = 0 t = 60 s x 1 = +200 mx f = -100 m x i = 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.

Velocity = distance/time 1. If a person is walking at 4 m/s, how far can he travel in 30 seconds? a) 120 meters b) 7.8 meters c).08 meters 2. A spaceship can move 100 meters in 2 seconds. What is the ship's velocity? a) 200 m/s b) 50 m/s c).002 m/s 3. A chicken runs across the street at a speed of 12 m/s. If the road is 36 meters across, how long does it take for the chicken to cross the road? a) 3 s b) 432 s c).333 s