Physics 211 Lecture 4: General 1Dimensional Motion

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Physics 211 Lecture 4 General 1-Dimensional
Motion
General Kinematic Equations

• General (most complicated) Case a a(t)
• Examples of a a(t)
• Exponential
• Sinusoindal
• Polynomial

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General Kinematic Equations (continued)

• Integrate to obtain velocity v ?a(t)dt
• Exponential
• Sinusoindal
• Polynomial

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General Kinematic Equations (continued again)

• Integrate again to obtain position x ?v(t)dt
• Exponential
• Sinusoindal
• Polynomial

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Constant Acceleration Kinematic Equations

• Replace a a(t) with a constant as shown
  above.
• Acceleration a C
• Velocity (integrate)
• Position (integrate again)
• What about free fall? Use a -g where g9.8m/s2

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Constant Acceleration defining average velocity
Note see book, page 36
Average Velocity - Mathematically
Average Velocity - Graphically
v
t
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Constant acceleration - Velocity as a Function of
Position rather than time
Note see book, page 36
Start with
Substitute eq. for t back into vel eq.
Determine t as a function of position Find
equation for t in terms of position
Simplify
Use quadratic equation to solve for t
Eliminate square root
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Example Ch2 22 745i BMW at 60mi/h stops in
121ft and at 80mi/h in stops in 211 ft. Find
average acceleration in a) 60mi/h case b) 80mi/h
case c) 80mi/hr to 60mi/h. Answer each in units
of mi/h/s and m/s2.
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Example Ch2 37Ball at rest accelerates at
0.5m/s2 down a 9m inclined plane. Next, ball
rolls up a 15m inclined plane to come to rest.
Find a) ball speed at bottom b) time to reach
bottom c)acceleration on second plane d) speed at
8m along second plane.
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Questions for Groups

• 2.12 Can eqs 2.9-2.13 be used if
• accel varies in time?
• a0?
• 2.14/15 One ball is thrown up at speed vi and
  another down with the same speed.
• Compare their accelerations while in the air
• Compare their velocities when they hit the ground
• 2.17 Ball dropped from window hits ground with
  speed v. Now drop again but with another ball
  thrown upwards simultaneously at that speed v.
  Do the balls pass each other at, above, or below
  the half way point? Why?