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Notes: 11.2 Speed & Velocity Speed A. The ratio of the distance an object moves to the amount of time the object moves. B. The SI unit of speed is m/s. However, it is useful to use km/h when talking about the speed of a car. Average Speed A. Average speed is computed for the entire duration of a trip. B. Average speed or “v” is the total distance traveled, “d”, divided by the time, “t”, it takes to travel that distance. C. Average Speed = Total distance / Total time or v = d/t. Example 1 While traveling on vacation, you measure the times and distances traveled. You travel 35 km in 0.4 hour, followed by 53 km in 0.6 hour. What is your average speed? What do we know? What do we want to know? What formula should we use? Solve! Example 2 A person jogs 4.0 kilometers in 32 minutes, then 2.0 kilometers in 22 minutes, and finally 1.0 kilometer in 16 minutes. What is the jogger’s average speed in kilometers per minute? What do we know? What do we want to know? What formula should we use? Solve! Example 3 A train travels 190 kilometers in 3.0 hours, and then 120 kilometers in 2.0 hours. What is its average speed? What do we know? What do we want to know? What formula should we use? Solve! Example 4 A car travels 85 km from Baltimore to Columbus, then 45 km from Columbus to Polaris. The total trip took 1.5 hours. What was the average speed of the car? What do we know? What do we want to know? What formula should we use? Solve! Example 5 A bicyclist travels for 1.5 hours at an average speed of 32 km/h. How far does the bicyclist travel in that time? What do we know? What do we want to know? What formula should we use? Solve! Instantaneous Speed A. Instantaneous speed is measured at a particular instant. B. Instantaneous speed, “v”, is the rate at which an object is moving at a given moment in time. Ex.) The speed of a car traveling on state route 256 is 55 miles per hour. Graphing Motion A. Time is graphed on the x - axis while distance is graphed on the y - axis. B. Slope = rise / run 1. In a distance time graph the slope is the change in the vertical axis value divided by the change in the horizontal axis value. 2. This is equal to average speed. C. A steeper slope on a distance - line graph indicates a higher speed while a less steep slope indicates a slower speed. Graphing Motion D. Graphs A and B show constant speed and graph C shows varying speed. 500 400 300 200 100 0 4 8 12 16 20 0 4 8 12 16 20 0 4 8 12 16 20 1. Graph A: Total Distance = ____________ Total Time = ____________ Average Speed = ____________ 2. Graph B: Total Distance = ____________ Total Time = ____________ Average Speed = ____________ D1 = _______ T1 = ________ V1 = _________ D2 = _______ T2 = ________ V2 = _________ D3 = _______ T3 = ________ V3 = _________ D4 = _______ T4 = ________ V4 = _________ D5 = _______ T5 = ________ V5 = _________ Total Distance = _____________ Total Time = _____________ Average Speed = _____________ Velocity A. Velocity is the speed and direction in which an object is moving. B. Since velocity has speed and direction it is a vector. 1. Smaller vectors represent slower speeds and longer vectors represent faster speeds. 2. Not only are vectors different sizes but they also point in different directions to represent the direction of a moving object. Velocity 3.Therefore a change in velocity can be the result of a change in speed, direction, or both. 4. An object moving in a straight line has constant velocity or uniform motion. Combining Velocities A. When an object is moving with more than one velocity we can add the velocities. 1. This is called vector addition. Vector Addition Ex.1) the velocity of the river relative to the riverbank (x) and the velocity of the boat relative to the river (y) combine. They yield the velocity of the boat relative to the riverbank (z). Vector Addition Ex.2) The relative velocities of the current (x) and the boat (y) are at right angles to each other. Adding these velocity vectors yields a resultant velocity.