# Practicing with Graphs

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Practicing with Graphs

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)

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)

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)

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)

The object moves toward the origin at a steady speed for 10s, then stands still for 10s.
V (m/s) t (s)

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)

An object that started at a slow speed is gradually speeding up at a constant rate.
V (m/s) t (s)

An object that started at a high speed, is gradually slowing down and then stops.
V (m/s) t (s)

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

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

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

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.

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.

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

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

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?

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?

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?

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?

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