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## Displacement

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**Position**Distance Displacement Chapter 2-1**Position**Position of an object is measured as a distance from a stationary reference point.**Frame of Reference**Examples: • The position of a moving car is relative to a tree.**Frame of Reference**• The Sun is the “Frame of Reference” for the planets.**Displacement**The length of the straight line drawn from a moving object’s initial position to its final position is called.**Language of Physics**Delta means “Change In”**ΔX = Xf– Xi**ΔX=change in position Xf = final position Xi= initial position**Distance vs. Displacement**Distance is how far an object moves over an entire trip. finish start Displacement is a straight-line path between an objects starting point and finish point. finish start**Distance vs. Displacement**DISTANCE = 10 mi + 7 mi = 17 mi 7 mi 10 mi Final position initial position 13 mi DISPLACEMENT = 13 mi**Describing Motion with Words**A physics teacher walks 4 meters East. Then he turns and walks 2 meters directly South, turns again to walk 4 m directly West, then finally heads 2 m North returning to his starting position. 2 m 2 m 4 m 4 m**Describing Motion with Words**• During the course of the teacher's motion, he has walked a distance of __12_meters. • However, since he has returned to his starting point, his displacement is __0__ meters.**Sign of Displacement**Positive- upward y(+) x Negative-to the left Positive-to the right (+) (-) (-) (+) (+) (-) Negative- downward**390 m**390 mm 130 m.**A soccer player changes position back and forth on the**field. In the diagram below each position is marked where the player reverses direction. The player moves from position A to B to C to D. • Find the distance and displacement of travel.**Describing Motion with Words**Solution Distance = 85 m Displacement = 55 m**Scalars**• A quantity that has only magnitude (a number value) Does not give direction object moves • Examples: speed v = 2.4 m/s distance x = 4 m**Vectors**• A quantity with both magnitude and direction • Examples: velocity (v= 2.4 m/s to the NORTH) displacement (x = 4 m left)**Speed vs Velocity:**different meaning - same equation Speed (scalar) • speed = distance/time v = x/t • scalar quantity-has only magnitude Velocity(vector) • velocity= displacement/time v = x/t • Vector quantity- has both magnitude and direction**Vectors Represented with Arrows**Displacements are represented by vector arrows. Each vector is drawn proportionate to its magnitude, and pointing in a direction. V= 50 m/s east V= 100 m/s east**Velocity**HOW FAST AN OBJECT IS MOVING**v = x / t**Average velocity = displacement / time • Units: meters/second (m/s) • Can be positive or negative depending on direction moved. • Average velocity, constant velocity, and speed are all the same equation. • Time can never be negative!**Constant Velocity**• The velocity does not change. Ex: A car with its cruise control on maintains a constant speed.**Instantaneous speed is speed at a particular moment in**time. • horse race photo finish • represented as a single point on a graph**If you graph position on the y-axis and time on the**x-axis, the slope of the line is equal to the average velocity. • Slope = rise = position = velocity run time**Slope of the line in a Position/Time Graph is**Velocity velocity position time Slope = rise = position = velocity run time**25**20 15 10 5 Constant Positive Velocity Zero Velocity POSITION (m) Constant Negative Velocity 0 5 10 15 20 25 TIME (sec)**Acceleration**• A change in velocity per unit time • It is a vector quantity and must have a direction • SI units for Acceleration m/s2**Acceleration**• Acceleration is the measure of how fast something speeds up, slows down or turns.**Accelerating Versus Decelerating**• A negative acceleration doesn’t always mean the object is slowing down. It could be moving in the negative direction.**Constant Acceleration**• Example: Velocity and displacement increase by the same amount each time interval**Instantaneous Acceleration**• Acceleration at an instant in time**Average Acceleration**a = vf – vi t Change in velocity divided by time taken to make this change**Slope of a graph describes the**objects motion**4 Kinematic Equations**• All the kinematic equations are related. • There is always more than one way to solve each problem. • In general though, one equation is generally easier to use then others.**Equations - Kinematic**• Vf = vi +at • ∆x=vi(t) + ½ a(t)2 • ∆x = ½ (Vi +Vf)∆t • Vf2 = Vi2 +2ax**Practice 2C**• #1. A car accelerates from rest to a speed of 23.7 km/h in 6.5 s. Find the distance the car travels. • Knowns? • vi = 0m/s, vf = 23.7km/h (6.58 m/s), t = 6.5 s • Unknowns? • Distance = ?, x= ? • Equation? • ∆x = ½ (Vi +Vf)∆t • Answer = ? • x = .5 (6.58)(6.5) =21.38 m**Practice**Heather and Matthew walk eastward with a speed of .98 m/s. If it takes them 34 min to walk to the store, how far have they walked? • Given: Speed = .98 m/s, time = 34 minutes (2040 sec) • Unknown: How far? Distance = ? • Equation: Speed = distance / time v = d/t • rearrange for distance d = vt • Substitute/Solve: d = (.98 m/s) (2040 s) d = 1999.2 meters