Chapter 5 A Mathematical Model of Motion

I. Graphing Motion in One Dimension

A. Position – Time graphs

1. Table 5-1 p 82

2. Graph 5-2 p 83

B. Instant – not a time interval

C. Interpolation & Extrapolation

1. Example problem p 83

D. Graphing 2 or more objects

1. Fig 5-3 p 84

2. Example problem p 84

E. Describing motion p 85

F. Uniform motion – equal displacements in equal time intervals

G. Slope on a distance vs time graph rise/run = ∆d/∆t = v

v = (df – di) / (tf – ti )

H. Let ti = 0 , then v = (df – di) / (t )

1. (df – di) = v (t)

2. df = di + v t

I. Example Problem p 88

PP(1-12)

II. Graphing Velocity in one dimension

A. Determining Instantaneous Velocity

1. On a d vs t graph, vinst is the slope of the line tangent at that instant

2. Fig 5-9 b p 90

B. Velocity vs time Graph

1. Area under the curve is ______

2. Fig 5-11 p 92

C. Example Problem p 92

93PP(13-16)

III. Acceleration

A. a = ( ∆v/∆t) p 56

B. The slope of a v vs t graph is ______

C. Fig 5-12 p 94

1.

2.

D. Fig 5-13 p 96 Note that v = 0 @ t =5 s in both cases. However, the slope is NOT zero, therefore, the acceleration is NOT zero.

97PP(17-22)

E. Calculating Velocity from Acceleration

1. a = ( ∆v/∆t) = (vf – vi ) /∆ t

2. a (∆ t ) = vf – vi

3. vf = vi + a∆ t

98PP(23-26)

F. Displacement of an object under constant Acceleration

1. d = (vi t) + ½ at2

2. vf2 = vi2 + 2ad

G. The BIG FOUR

1. v = ∆d/∆t

2. a = ( ∆v/∆t)

3. d = (vi t) + ½ at2

4. vf2 = vi2 + 2ad

H. Example Problem p 101

I. Example Problem p 102

103PP(27-30)

IV. Free Fall

A. Acceleration due to Gravity, g

1. g = 9.80 m/s2

2. If up is positive, then in free fall a = - g

B. Fig 5-18 p104

C. Ball thrown upward example

D. Fig 5-19 p105

E. Example Problem p 105

106PP(31-33)

Assignment:

107 RC (1-10)

108 AC (15, 16, 19 – 25)

109 P (27, 28, 33, 34, 40, 44, 45, 47, 50, 54, 58, 62, 69, 73, 74, 75)