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**Practicing with Graphs**

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**Plot the motion on a DISPLACEMENT-TIME graph**

An object moves at a constant velocity, then stops, then moves at a faster constant velocity. d (m) t (s)

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**Plot the motion on a DISPLACEMENT-TIME graph**

An object moves at a constant velocity, then stops, then moves backwards at a constant velocity. d (m) t (s)

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Sketch velocity vs. time graphs corresponding to the following descriptions of the motion of an object. The object is standing still. V (m/s) t (s)

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**The object is moving away from the origin at a constant (steady) speed.**

The point from which motion is measured. Motion going away from the origin is positive and motion towards the origin is considered negative (or in the backwards direction) V (m/s) t (s)

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**The object moves toward the origin at a steady speed for 10s, then stands still for 10s.**

V (m/s) t (s)

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The car driving down the road moves away from you (the origin) at a steady speed for 10s, reverses direction and comes driving back toward you at the same speed. V (m/s) t (s)

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**An object that started at a slow speed is gradually speeding up at a constant rate.**

V (m/s) t (s)

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**An object that started at a high speed, is gradually slowing down and then stops.**

V (m/s) t (s)

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Draw the velocity vs time graphs for an object whose motion produced the position vs time graphs shown below at left.

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Draw the velocity vs time graphs for an object whose motion produced the position vs time graphs shown below at left.

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Draw the velocity vs time graphs for an object whose motion produced the position vs time graphs shown below at left.

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**The displacement of an object can also be determined from a velocity vs time graph.**

The displacement of the object can be found by finding the area under the curve. According the graph at the left, the total displacement traveled during the 4 seconds was 4 m. Area = l x w = 4 s x 1 m/s = 4 m Compare your calculated answer with the original displacement vs time graph.

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**Calculate the total displacement using the velocity vs time graph shown below.**

Area = l x w = 2 m/s x 1 s = 2 m Area = l x w = 0.5 m/s x 4 s = 2 m Total displacement = = 4 m Compare this answer with the original displacement vs time graph.

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Quick Quiz 1) What is the equation for average velocity???

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**Quiz 2) How do we find the acceleration from a velocity-time graph?**

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Quick Quiz 3) If an object accelerated at a constant rate so that it went from a speed of 0 m/s to a speed of 10 m/s, what was its average speed during this time?

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Quick Quiz 4) What is the equation for determining displacement when an object is moving at a constant speed? 5) What is the equation for determining displacement when an object is moving with an acceleration?

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6) What is the acceleration of a car that goes from a speed of 12 m/s to a speed of 28 m/s in a time of 8 seconds?

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7) If gravity accelerates an object at a rate of 10 m/s2 and you drop an object from rest how fast will it be going after 7 seconds?

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**Answers 7) a=v / t 1) Average speed = (total displacement)/ time**

2) Find the slope (rise/run) 3) 5 m/s …… Or in other words find the midpoint between the initial speed and final speed 4) d = vavgt 5) d = vavgt……. Just remember to make sure you are using AVERAGE speed, not the final speed. 6) 2 m/s2 Acc = (v)/ t = (16 m/s)/ 8 s = 2 m/s2 7) a=v / t v = at = 10 m/s2 x (7 s) = 70 m/s

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