Motion in One Dimension Kinematics Distance vs Displacement

Motion in One Dimension Kinematics

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

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) 1. 0 2. 0 Position (m) 3. 0 6. 0

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. • The total distance traveled was (52 + 42 + 25)m = 119 m The total displacement is 99 Paces, 28 o, N of W

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

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

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

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

Constant Velocity • Average velocity is the same for all time intervals. Time (s) 1. 0 Velocity (m/s) 30. 2. 0 30.

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. 0 35 2. 0 55

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

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

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 s x 1 Km x 3600 s 1000 m 1 h = 72 km/h

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 ∆t t 2 - t 1 2. 0 h 6. 5 Km h = 6. 5 km/h x 1000 m x 1 h = 1. 8 m/s 1 Km 3600 s

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 = dt = d 1 + d 2 + d 3 tt 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

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

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.

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

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)

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