Transcript Representing Motion in a Variety of Ways

Representing Motion in a Variety of
Ways
Graphs:
- Allows us to interpret motion without even
seeing the motion occur
What was the object’s velocity (not speed)
from 0-2 sec?
• +2 m/s
• Can we derive an equation for velocity from
this graph? Or any other x-t graph?
X f = vt + xi
X f – Xi = vt
(4𝑚 − 0𝑚)
𝑉=
2𝑠
𝑉=
4𝑚
= 2 𝑚/𝑠
2𝑠
(𝑋𝑓 −𝑋𝑖 )
𝑡
=V
∆𝑋
𝑉=
𝑡
Position-Time Graphs (x-t)
Velocity from 2-3 seconds?
0𝑚
𝑉=
= 0 𝑚/𝑠
1𝑠
Velocity from 3-7 seconds?
𝑉=
(𝑋𝑓 −𝑋𝑖 ) (0 𝑚−4 𝑚)
=
𝑡
4𝑠
=
−4 𝑚
4𝑠
= −1 𝑚/𝑠
Motion Maps
Another way to represent an object’s motion
• We can go back and forth between graphs and motion maps to represent the
same motion
• To make a motion map, you need to draw an arrow representing positive
direction
Constant positive velocity
X
Beginning of the arrow is
the reference point
(origin)
If the object is moving, its position will change over time. If the object is stationary, its
position will remain the same as time increases
• On a motion map, this is illustrated by a single dot on the position arrow
Motion Maps
Object is stationary
X
An object’s constant velocity is indicated by 2 things:
• The displacement between the points are constant (change in position is equal)
• Arrows indicating the object’s velocity are the same length
Constant positive velocity
X
If the object is stationary, then the velocity is zero and there is not an arrow indicating velocity
X
More than one object
How do we know which object
is traveling faster?
• slope: remember, slope =
velocity
• Steeper the slope, faster the
velocity
B
X (m)
A
Object B has a greater displacement (change in
position) than A IN THE SAME AMOUNT OF TIME
2
t (sec)
Review from yesterday
∆𝑥 = (𝑥𝑓 − 𝑥𝑖 )
Slope
∆𝑥
=𝑡
= 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
Y-intercept = starting
position
Velocity IS NOT THE SAME as speed
Speed
• How fast
X
X
Velocity
• How fast
• direction
Consider the following x-t graphs
•
Rank these situations from greatest to least based on which shows the greatest displacement
during the time from 0 to 10 sec. Use the > and = signs, but do not use the < sign.
•
Rank these situations from greatest to least based on which shows the greatest distance traveled
during the time from 0 to 10 sec. Use the > and = signs, but do not use the < sign.