Physics 2211: Lecture 3 Todays Agenda

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Physics 2211 Lecture 3Todays Agenda

• 1-D motion Kinematics
• Motion Diagrams and Graphs
• Uniform motion vs. Non-uniform Motion
• (Instantaneous) Velocity

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Motion in 1 dimension

• Vectors are not needed! Just use a or sign
  for x(t), v(t) and a(t)

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A particle that moves in a straight line with a
constant speed is said to move in Uniform
Motion The slope of the x(t) vs t graph of a
particle moving with uniform motion is Several
consecutive regions of uniform motion can form a
motion that is piece-wise uniform
motion Motion that is not uniform is
non-uniform motion.
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Mechanics Vocabulary

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Mechanics Vocabulary

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Graph (Position vs Time)


Motion Diagram
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Watch how average velocity changes as we decrease
??t
For very small time intervals, the average
velocity vectors are almost the same length!!
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If x(t) and v(t) are in the same direction (say
both ), then x(t) is increasing. If they have
opposite signs, then x(t) is decreasing. If
v(t) and a(t) are in the same direction (say both
), then v(t) is increasing. If they have
opposite signs, then v(t) is decreasing
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More generally, for any position vector r(t) and
velocity vector v(t) the velocity causes the
magnitude of the position vector to increase
if More to the point the dot product of the
velocity vector and a unit vector in the
direction of r yields the component of v in the
direction of r.
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Average Velocity Graphical Interpretation

• Velocity is the rate of change of position
• Average velocity in the time ??t t2 -
  t1 is

x2
??x
slope of line connecting x1 and x2.
x1
t1
t2
??t
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Instantaneous Velocity

• Consider limit

??x
??t
Instantaneous velocity v is defined as
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Relating Graphs
Position vs Time
Velocity vs Time
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Which graph best describes the motion diagram?
PRS QUESTION 1
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3
1
2
4
Which green curve of v(t) best describes the blue
curve of x(t)?
PRS QUESTION 2
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Finding Position from Velocity
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Finding Position from Velocity (continued)

• Another way v dx / dt dx v dt
• Integrate to get

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At the end of any time interval tf , x is what it
was at time ti plus the sum of all the changes
from ti to tf.
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Example 2.8

• What is the displacement during the first three
  seconds?

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2
1
4
3
Which blue x(t) graph best describes the green
v(t) graph? (at t0, the particle is at x -10 m)

• PRS QUESTION 3

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Recap

• Motion Diagrams Graphs Uniform motion vs
  Non-Uniform Motion (Instantaneous) Velocity
• Next
  Lecture
• Section 2.5 in Knight (Constant Acceleration)