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Jan 02, 2016

Motion in One Dimension

Kinematics

Distance vs. Displacement

Distance how far youve traveled Scalar quantity - 20 m

Displacement shortest distance traveled from starting point to end point. Vector quantity 20 m, 40o, N of W

Instantaneous PositionWhere an object is located at one and only one time.At 1.0 s, object is at 3.0 mAt 2.0 s, object is at 6.0 m

Remember the example? Change the paces to meters (m).Walk due west for 52 m, then walk 30.0o 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, 28o, N of W

Speed

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

VelocityVelocity is how fast an object is moving in a certain direction. Vector quantity = 30 km/h, 45o, 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 VelocityAverage velocity is the same for all time intervals.

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.

Average Velocity I Change in displacement over a given time interval. Equation: V = d = d2 d1 t t2 - t1

Unit of measurements: m/s, cm/s, ft/s, km/h, and mi/h

Average SpeedTotal distance traveled over total time

Equation: V = dt = d1 + d2 +.. tt t1 + t2 + ..

Units of Measurements: m/s, cm/s, ft/s, km/h, and mi/h

ConversionsKilo = 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

Example 1A person walks 13 km in 2.0 h. What is the persons average velocity in km/h and m/s?

V = d = d2 d1 = 13 km = 6.5 km/h t t2 - t1 2.0 h

6.5 Km x 1000 m x 1h = 1.8 m/s h 1 Km 3600 s

Example 2A car traveled 2.0 mi. in 0.2 h, 5.0 mi in 0.6 hand 15.0 mi in 1.0 h. What was the average speed of the car?V = dt = d1 + d2 + d 3 tt t1 + t2 + t3

= 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 3A 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 4A 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 AccelerationChange in velocity over a period of time.

a = V = V2 V1 t t2 - t1

Units of measurements: m/s2, cm/s2, ft/s2 km/h2, and mi/h2

Direction of AccelerationPositive 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 ExampleAn Indy-500 race cars 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 V2 = +36.0 m/s t = 4.0 s a = V = +36.0 m/s +4.0 m/s = 8.0 m/s2 t 4.0 s

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