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Motion A change in position relative to some reference point during a period of time.

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**Speed Rate at which an object moves Speed = distance/time**

Units: m/sec, km/hr, mi/hr. d s t

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**Types of Speed Instantaneous Speed – speed at a given instant.**

Average Speed = ∆ distance/ ∆ time. Describes speed of motion when speed is changing. Constant Speed – speed that doesn’t change.

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Speed Problems What is the speed of a cyclist who travels 50 meters in 25 seconds? S = d/t 50 m/25 s 2 m/s You are in a car traveling an average speed of 60 km/hr. The total trip is 240 km. How long does the trip take? t = d/s 240 km/60 km/hr 4 hrs.

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**Distance -Time Graphs Time (sec) Time (sec) Time (sec) Time (sec)**

Distance (m) Distance (m) Time (sec) Time (sec) Distance (m) Distance (m) Time (sec) Time (sec)

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**Velocity Speed in a given direction.**

Uses: Navigation (airplanes, ships), weather, etc. Vector quantity – represented graphically by arrows ( ). Length = magnitude Arrowhead = direction

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Velocity Problem If you row a boat upstream at 10 km/hr and the river has a downstream velocity of 5 km/hr, you are actually moving at what velocity? = 5 km/hr downstream 10 km/hr upstream 5 km/hr upstream

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**Acceleration Rate of change in velocity.**

Really a description of “how fast you can go in a certain amount of time”. Good acceleration is being “quick to change”.

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Acceleration Examples: speeding up (+ acc.), slowing down (- acc.), or changing direction. Acc. = final velocity – original velocity/time. Units: m/sec/sec Represented by a Velocity – Time Graph

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**Velocity vs. Time Graphs**

Time (sec) Velocity (m/s) Time (sec) Velocity (m/s) Time (sec) Velocity (m/s) Time (sec) Velocity (m/s)

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Acceleration Problem A car increases its speed from 60 km/hr to 80 km/hr in 4 seconds. What is the car’s acceleration? Acc = Δ velocity time 80 km/hr – 60 km/hr 4 sec. 5 km/hr/sec. 1st second – 65 km/hr 2nd second – 70 km/hr 3rd second – 75 km/hr 4th second – 80 km/hr

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**Rates of Motion Table Rates Definition Equation Unit Graph Speed**

Velocity Acceleration

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**Gravitational Acceleration**

Acceleration on an object caused by gravity.

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Falling Objects Free fall – considers only gravity & neglects air resistance. All falling objects accelerate at the same rate, regardless of their masses. - 9.8 m/sec/sec or 32 ft./sec/sec. on earth. - velocity increases 9.8 m/s each second. - distance fallen – increases mathematically

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**Uniform Motion Equations**

Instantaneous speed vf = vi + at Distance fallen d = vit + ½at2 Average speed v = vi + vf 2

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**Objects Thrown Straight Up**

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Graphing Free Fall Distance (m) velocity (m) Time (sec) Time (sec)

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**Air Resistance on Falling Objects**

Air resistance noticeably alters the motion of things like falling feathers or pieces of paper. Less noticeably on more compact objects. e.g. stones, balls

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Motion In One Dimension by: Heather Britton. Motion In One Dimension Kinematics - the study of how objects move Frame of reference - what you are comparing.

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