Physics 151 Week 4 Day 3
Topics
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Motion Diagrams
Motion Graphs
Area under a curve (velocity to position)
Constant acceleration equations
Motion Diagrams (a.k.a. Motion Maps)
The motion diagrams below show an initial point 0 and a final point 1. A
pictorial model would define five symbols, x0 and x1 (or y0 and y1), v0x and
v1x, and ax. Determine whether each of these quantities is positive,
negative, or zero. place either +, --, or 0 in each cell of the table below.
These are motion diagrams with axes. For this
problem, you have to figure out which positions,
velocity components and acceleration components
are negative (--), positive (+), or zero for one
motion interval.
– "0" on the axis indicates the origin and the "x" or "y"
indicates the positive x or y direction respectvely.
– The "0" on the motion diagram represents the initial
position of the object for the motion interval shown.
– The "1" on the motion diagram represents the final
position of the object for the motion interval shown.
A
x0
x1
V0x
v1x
ax
Slide 2-4
Motion Maps for + / - vx and ax
Slide 2-4
Motion Graph Demonstrations
Slide 2-4
Velocity Graph => Acceleration Graph
vx  slope of x vs. t graph
ax  slope of vx vs. t graph
Slide 2-4
x = area under vx vs. t graph
1
1
 x  area  b h   t  vx
2
2
Slide 2-4
vx = area under ax vs. t graph
 vx  area  b h   t ax
Slide 2-4
General Motion Model Graph Relationships
vx  slope of x vs. t graph
ax  slope of vx vs. t graph
x  area under vx vs. t graph
vx  area under ax vs. t graph
Slide 2-4
Constant Acceleration Equations
 vx  area  b h   t ax
 vx  a x  t
 v1x  v0 x  ax  t
(equation 1)
x  area under vx vs. t
x  Area1 (square)  Area2 (triangle)
1
1
x  bh1  bh2   t v0 x   t v1x
2
2
1
x   t v0 x   t  a t 
2
1
 x  v0 x  t  ax  t 2 (equation 2)
2
Area 2
Area 1
Slide 2-4