1motion1d_FA10 - Distance and Displacement The displacement...

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1 Distance and Displacement The displacement of an object is defined as the vector distance from some initial point to a final point. It is therefore distinctly different from the distance traveled except in the case of straight line motion. 1 2 x x x = Δ x 0 x Example: Distance is the total length that an object has moved. If I walk 2 km north, then 1 1 km south, the distance I have moved is 3 km. On the other hand displacement is the net change in position. My displacement is only 1 km. Frame of Reference Any measurement of position, distance, and/or speed must be made from an origin , which is a starting point from which to take further observations and measure, collect, and analyze our experiences. Velocity The distance traveled divided by the time is called the speed, while the displacement divided by the time defines the average velocity Average velocity is the displacement/(elapsed time). The rate over which displacement changes: Example: t x t t x x Δ Δ = = 1 2 1 2 v 2 If it takes me 45 minutes to walk two km west, and one km east, then the average speed is 3.0/0.75 = 4.0 km/hour average velocity is 1.0/.75 = 1.3 km/hour.
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2 Speed Problem : If a dog jogs for 1.5 hours at an average speed of 2.22 m/s, how far does he go? How far means what is the distance he goes. 3 Instantaneous velocity t x t Δ Δ = Δ 0 lim v (instantaneous velocity)=derivative of position w.r.t. time also: slope of tangent line to x vs. t curve v = v (instantaneous speed)=(magnitude of instantaneous velocity) 4
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This note was uploaded on 11/22/2010 for the course PHYS 1146 taught by Professor Balasubramamaheswaran during the Spring '10 term at Northeastern.

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1motion1d_FA10 - Distance and Displacement The displacement...

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