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Relationship between time, displacement, velocity, acceleration. Kinematic

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Relationships between the variables (s, d, t) This is the scalar relationship between speed, distance, and time. s = speed d = distance t = time speed = distance / time s = d / t

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A car traveled 300 miles in 10 hours, determine the speed of the car.

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distance = 300 miles time = 10 hours s = distance / time = 300 miles / 10 hours = 30 miles / hr.

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Relationships between the variables (v, d, t) This is the vector relationship between velocity, displacement, and time. v = velocity d = displacement t = time velocity = displacement / time

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A car traveled 300 miles north in 10 hours, determine the velocity of the car. displacement = 300 miles time = 10 hours Velocity = displacement / time = 300 miles / 10 hours = 30 miles / hr. north

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Variations on the same equation speed = distance / time distance = speed time time = distance / speed velocity = displacement / time displacement = velocity time time = displacement / velocity

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units Units of speed m/sft/s km/hr(kph)miles/hr (mph) Units of velocity m/s northft/s south km/hr westmiles/hr east

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How units are related speed = distance / time distance - meters time - seconds speed = meters / seconds

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How units are related distance = speed time speed - meters / seconds time - seconds distance = meters / seconds seconds = meters

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How units are related time = distance / speed distance = meters speed = meters / seconds time = meters / (meters / seconds) = seconds

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Position and average velocity Another way to calculate for velocity is to use an object’s position with respect to time. When the object is at point A, its position is 2 meters after 3 seconds and point B is 5 meters after 8 seconds. Displacement (m) Time (s) A B rise run (3, 2) (8, 5)

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Position and velocity Think of slope where we have

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Velocity and average acceleration Velocity (m/s) time (s) A B rise run (3, 2) (8, 5) When the object is at point A, its velocity is 2 m/s after 3 seconds and point B is 5 m/s after 8 seconds.

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Velocity and acceleration Think of slope where we have

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Practice problems 1. A person was running south at a rate of 3 m/s. This person has been running for 3 minutes. How far has this person traveled in the 3 minutes?

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2. During the first 10 seconds, a car traveled a distance of 800 meters. What is the average speed of the car?

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3. If the cheetah has been running at a speed of 30 m/s for 8 seconds, how far has the cheetah traveled in this span of time?

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4. A car slows from a velocity of 40 m/s to 25 m/s in 8 seconds. What is the average acceleration of the car?

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5. If the average acceleration of an object is 3 m/s 2 over a span of time of 2 seconds, what is the change in velocity over the 2 seconds?

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