What You Should Know When All Is Said and Done

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Unit II Objectives

What you should know when all is said and done

1.You should be able to determine the average velocity of an object in two ways:

a.determining the slope of an x vs t graph.

b.using the equation

2.You should be able to determine the displacement of an object in two ways:

a.finding the area under a v vs t graph.

b.using the equation

3.Given an x vs t graph, you should be able to:

a.describe the motion of the object (starting position, direction of motion, velocity)

b.draw the corresponding v vs t graph

c.draw a motion map for the object.

d.determine the average velocity of the object (slope).

e.write the mathematical model which describes the motion.

4.Given a v vs t graph, you should be able to:

a.describe the motion of the object (direction of motion, how fast)

b.draw the corresponding x vs t graph

c.determine the displacement of the object (area under curve).

d.draw a motion map for the object.

e.write a mathematical model to describe the motion.

UNIT II Worksheet 1 / UNIT II Worksheet 2 / UNIT II Worksheet 3

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UNIT II Worksheet 1

1.Consider the position vs. time graphs below for cyclists A and B.

a.Do the cyclists start at the same point in either graph? If not, which is ahead? How do you know?

b.Which cyclist is ahead at t = 7s in each graph? How do you know?

c.Which cyclist has the greater speed at t = 3s in each graph? How do you know?

d.Are the cyclists’ velocities equal at any time in either graph? How do you know?

e.What is happening at the intersection of lines A and B in each graph?

2.Robin, roller skating down a marked sidewalk, was observed to be at the following positions at the times listed below:

t (s) / x (m)
0.0 / 10.0
1.0 / 12.0
2.0 / 14.0
5.0 / 20.0
8.0 / 26.0
10.0 / 30.0

a.Plot the position vs. time graph for the skater.

b.How far from the starting point was she at t = 6 s? How do you know?

c.Write a mathematical expression to describe the graph in (a).

d.Was her speed constant for the entire time? How do you know?

3.Suppose our skater was observed in a second trial. The following data were obtained:

t (s) / x (m)
0.0 / 0.0
2.0 / 6.0
4.0 / 12.0
6.0 / 12.0
8.0 / 8.0
10.0 / 4.0
12.0 / 0.0

a.Plot the position vs. time graph for the skater.

b.What is happening during the time interval from t = 4 s to t = 6 s? How do you know?

c.What is happening during the time interval from t = 6 s to t = 12 s? How do you know?

d.Determine the skater's average speed from t = 0 s to t = 12 s.

e.Determine the skater's average velocity from t = 0 s to t = 12 s.

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UNIT II Worksheet 2

Sketch the velocity vs. time graph that corresponds to each of the following descriptions of an object’s motion.

1.The object is moving in the negative direction with a constant speed. /
2.The object is standing still. /
3.The object moves in the negative direction with a constant speed for 10 s, then stands still for 10 s. /
4.The object moves in the positive direction with a constant speed for 10 s, then reverses direction and moves with the same constant speed for 10 s. /

Draw the velocity vs. time graph for each object whose motion produced the position vs. time graph shown.

5.
/
6. /
7.
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UNIT II Worksheet 3

x vs t Graph / v vs t Graph / Written Description / Motion Map
x vs t Graph / v vs t Graph / Written Description / Motion Map
Object moves with constant positive velocity for 4 seconds. Then, it stops for 2 seconds and returns to the initial position in 2 seconds.
Object A starts 10m to the right of the origin and moves to the left at
2 m/s.
Object B starts at the origin and moves to the right at 3m/s.