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)