1 – D Motion. We begin our discussion of kinematics (description of motion in mechanics) Simplest case: motion of a particle in 1 – D Concept of a particle : idealization of treating a body as a single point (we get close to doing this by pinpointing the “license plate of a car,” etc.)
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+x
Position vectors (keep track of position of car)
Displacement vector (change in position from point 1 to point 2)
Position and Displacement(north)
Park Ave. (reference point or origin)
William St.
(point 1)
Central Ave. (point 2)
CQ1: Consider the figure below that shows three paths between position 1 and position 2. (Path C is a half circle.) Which path would result in the greatest displacement for a particle moving from position 1 to position 2?
Stopwatch measures time between position 1 and position 2. (Path C is a half circle.) Which path would result in the greatest displacement for a particle moving from position 1 to position 2? t1
Stopwatch measures time t2
(average speed = total distance traveled / time to travel that distance)
Velocity+x
Park Ave. (reference point or origin)
William St. (point 1)
Central Ave. (point 2)
Stopwatch measures time between position 1 and position 2. (Path C is a half circle.) Which path would result in the greatest displacement for a particle moving from position 1 to position 2? t2
Stopwatch measures time t1
Velocity+x
Park Ave. (origin)
William St. (point 2)
Central Ave. (point 1)
Trip #1 between position 1 and position 2. (Path C is a half circle.) Which path would result in the greatest displacement for a particle moving from position 1 to position 2?
Trip #2
vaveis the same for both trips!
t1
t2
Velocityx
Central Ave.
William St.
time
Park Ave.
Slope = instant. velocity at time between position 1 and position 2. (Path C is a half circle.) Which path would result in the greatest displacement for a particle moving from position 1 to position 2? t2
Slope = instant. velocity at timet1
t1
t2
Instantaneous Velocityx
Central Ave.
William St.
time
Park Ave.
(I’m right back where I started!)
CQ2: The graph below represents a particle moving along a line. What is the total distance traveled by the particle from t = 0to t = 10seconds?
Slope = average acceleration line. What is the total
v2
v1
t1
t2
Accelerationv
t
Slope of tangent line = instantaneous acceleration line. What is the total
v1
t1
Accelerationv
t
Same sign
Oppositesign
(for example, going slower in reverse)
PHYSLET #7.1.1, Prentice Hall (2001)
v
Constant acceleration means constant rate of increase for v
t
Average value of position vs. time graph? (Assume that the positive v:
(since v is a linear function)
Also, by definition:
Setting (2) = (3), and using (1), we get:
Constant Acceleration(takes form of equation of a line:y = b + mx)
v
v
at
v0
v0
t
(independent of t)
(independent of a)
Motion Graphs Interactive
CQ4: The graph below represents a particle moving along a line. When t = 0, the displacement of the particle is 0. All of the following statements are true about the particle EXCEPT:
Animation and solution details given in class.
ActivPhysics Problem #1.8, Pearson/Addison Wesley (1995–2007)
+y(up)
then =
0
0
then =
+y(down)
+ situation are both the instantaneous velocity and the acceleration zero? y
443 m
How long would it take for Tom Petty to go “Free-Fallin’” from the top of the Sears Tower in Chicago? (Of course there is a safety net at the bottom.)
How fast will he be moving just before he hits the net?
(negative sign means downward direction)
CQ6: A pebble is dropped from rest from the top of a tall cliff and falls 4.9 m after 1.0 s has elapsed. How much farther does it drop in the next 2.0 seconds?
v
Free fall only
vtis called the “terminal velocity”
vt
Including air resistance effects
t