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Motion in One Dimension Kinematics

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Distance vs. Displacement Distance – how far you’ve traveled Scalar quantity - 20 m Displacement – shortest distance traveled from starting point to end point. Vector quantity – 20 m, 40 o, N of W

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Instantaneous Position Where an object is located at one and only one time. At 1.0 s, object is at 3.0 m At 2.0 s, object is at 6.0 m Time (s)Position (m) 1.03.0 2.06.0

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Remember the example? Change the paces to meters (m). Walk due west for 52 m, then walk 30.0 o North of West for 42 m, and then walk due north for 25 m.Walk due west for 52 m, then walk 30.0 o North of West for 42 m, and then walk due north for 25 m. The total distance traveled wasThe total distance traveled was (52 + 42 + 25)m = 119 m 99 Paces, 28 o, N of W The total displacement is 99 Paces, 28 o, N of W

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Speed Speed is how fast an object is moving. Scalar quantity = 30 km/h

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Velocity Velocity is how fast an object is moving in a certain direction. Vector quantity = 30 km/h, 45 o, S of E

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Direction of Velocity (+) Velocity is positive (+) if moving due east or due north. N E

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Direction of Velocity (-) Velocity is negative (-) is moving due west or due south. W S

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Constant Velocity Average velocity is the same for all time intervals. Time (s) Velocity (m/s) 1.030. 2.030.

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Instantaneous Velocity Speed and direction at one and only one time. At 1.0 s, the instantaneous velocity is 35 m/s. At 2.0 s, the instantaneous velocity is 55 m/s. Time (s) Velocity (m/s) 1.035 2.055

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Average Velocity I Change in displacement over a given time interval. Equation: V = ∆d = d 2 – d 1 ∆t t 2 - t 1 Unit of measurements: m/s, cm/s, ft/s, km/h, and mi/h

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Average Speed Total distance traveled over total time Equation: V = d t = d 1 + d 2 +.. t t t 1 + t 2 + ….. Units of Measurements: m/s, cm/s, ft/s, km/h, and mi/h

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Conversions Kilo = 1000 1 Km = 1000 m 1 mi. = 1609 km 1 h = 3600 s Change 20.0 m/s to Km/h 20.0 m x 1 Km x 3600 s = 72 km/h s 1000 m 1 h

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Example 1 A person walks 13 km in 2.0 h. What is the person’s average velocity in km/h and m/s? V = ∆d = d 2 – d 1 = 13 km = 6.5 km/h ∆t t 2 - t 1 2.0 h 6.5 Km x 1000 m x 1h = 1.8 m/s h 1 Km 3600 s

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Example 2 A car traveled 2.0 mi. in 0.2 h, 5.0 mi in 0.6 h and 15.0 mi in 1.0 h. What was the average speed of the car? V = d t = d 1 + d 2 + d 3 t t t 1 + t 2 + t 3 = 2.0 mi + 5.0 mi + 15.0 mi = 12 mi/h = 10 mi/h 0.2 h + 0.6 h + 1.0 h

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Example 3 A car traveled 2.0 h at a speed of 50 mi/h and 4.0 h at 75 mi/h. Calculate the average speed. V = (2.0 h x 50. mi/h) + (4.0 h x 75 mi/h) 2.0 h + 4.0 h V = 67 mi/h

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Example 4 A toy train starts at 0 m and runs around the 1.0 m track in 30 s. train stops at the starting point. What was its average speed? V = 1.0 m/30 s = 0.03 m/s What was its average velocity? V = 0 m/s. It stopped at its starting point. The change in displacement is 0.

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Average Acceleration Change in velocity over a period of time. a = ∆V = V 2 – V 1 ∆t t 2 - t 1 Units of measurements: m/s 2, cm/s 2, ft/s 2 km/h 2, and mi/h 2

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Direction of Acceleration Positive if the change in velocity is positive. ∆V = 40 m/s – 20 m/s = + 20 m/s Acceleration is increasing. Negative if the change in velocity is negative. ∆V = 20 m/s – 40 m/s = -20 m/s Acceleration is decreasing. (decelerating)

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Acceleration Example An Indy-500 race car’s velocity increases from +4.0 m/s to +36 m/s over a 4.0 s period. What is its average acceleration? V 1 = +4.0 m/s V 2 = +36.0 m/s ∆t = 4.0 s a = ∆V = +36.0 m/s – +4.0 m/s = 8.0 m/s 2 ∆t 4.0 s

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