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One Dimensional MotionReview of the basics
AP Physics
Terms
Displacement vs. Distance
Displacement: Change in position (vector)
Distance: How far an object has traveled (scalar)
Terms
Velocity vs. SpeedVelocity: Rate of the change in position
(vector)
Speed: Rate of distance covered (scalar)
Terms
Acceleration vs. Acceleration?Acceleration: The rate at which velocity
changes (vector) This could be a change in:
• Speed• Direction• Speed and direction
Position vs. Time Graph
The slope of
an x vs. t
graph is the
velocity
What are the velocities?
rise 2 0(a) 2 /
run 1 0(b) 0 m/s
(c) 1 m/s
0 3 3(d) 1.5 /
5 3 2
xm s
t
m s
Average Velocity on an x-t graph
Average velocity vs instantaneous velocity
on an position – time graph
As the two points P1 and P2 get closer, the time frame (∆t) gets smaller and smaller approaching zero. Eventually you are considering a moment in time rather than a period of time. Graphically, you are looking at the slope of a tangent line rather than the slope of the line connecting two points.
Instantaneous Velocity on an x-t graph
Velocity vs. Time Graph
The slope of a v vs. t graph is the acceleration
The area between the curve and the horizontal axis of a v vs. t graph is the displacement
Instantaneous Acceleration vs Average Acceleration from a v-t graph
As the two points P1 and P2 get closer, the time frame (∆t) gets smaller and smaller approaching zero. Eventually you are considering a moment in time rather than a period of time. Graphically, you are looking at the slope of a tangent line rather than the slope of the line connecting two points.
What are the accelerations and displacements?
2(A) a=2 m/s
1x=
2(.5)(5)(10) 25
bh
m
(B) a=0
x = LW
(10)(10) 100m
2(C) 0.5 /
1
2(5 10) (.5 10 5) 75
a m s
x LW bh
x x x m
Acceleration vs. Time Graph
The slope means NOTHING The area between the curve and the horizontal
axis is the change in velocity
a
t-10 m/s/s
10 s
100 /v m s
Important
Acceleration tells us how fast velocity changes
Velocity tells us how fast position changes
Falling Bodies, thrown up objects, and the y-direction
All things fall at the same rate (neglecting air resistance)
On earth that rate is 9.80 m/s2DOWNWATCH THE DIRECTION!The name of that acceleration is
Gravitational acceleration
Thanks!
This is a good quick review for kinematics. However, it is just a review not the end all be all of kinematics.