Average acceleration vector is in the direction of the change in velocity over the time interval Δt
1
Can an object accelerate with a constant speed?
Consider a car driving on a circular track at a constant speed of 12m/s. What are the velocity vectors at these 2 locations?
Note the speed is 12m/s in both cases, but the velocity is different since the direction has changed
2
Acceleration
Velocity vector is always in the direction of motion; acceleration vector can point anywhere:
3
Clicker Quiz
A car travels in the east direction and its
velocity increases as it continues moving
easterly. The acceleration of the car is in
which of the following directions?
A) Eastward
B) Westward
C) Northward
D) Southward
4
Clicker Quiz
If the acceleration of an object is always directed perpendicular to its velocity, then A) the object is speeding up.
B) the object is slowing down.
C) the object is moving with a constant velocity.
D) the object is turning.
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y
moving object in three-dimensional space
p
Point P will move around in space
Time dependent Position vector defines the location from the origin
x
z
write down the vector in its most general form The vector decomposed into 3 independent vectors.
Velocity is the time rate change of displacement Acceleration is time rate change of velocity
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y
We have a point P moving in three‐dimensional space p
x
z
the entire
behavior of
the object as
it moves
along its
projection
along the x
axis.
the entire
behavior of the
object as it
moves along its
projection
along the y
axis.
the entire
behavior of the
object as it
moves its
projection
along the z
axis.
the three‐dimensional motion we have cut into 3 one‐dimensional motions.
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if I throw a tennis ball, the whole trajectory is in one plane in the vertical plane.
Even though it is in three dimensions we can always represent it by two axes,
vertical y axis and a horizontal x axis.
The three‐dimensional problem often becomes a two‐dimensional problem.
8
1-D Constant Acceleration
1-D Constant Acceleration in y
9
Motion in Gravitational field
y
x
10
DEMO Ballistic Car
46:02 MIT Golf Ball
11
Relative Motion An object may appear to have one motion to one observer and a different motion to a second observer, depending on how the two observers are moving with respect to one another. In other words, the velocity of an object is measured relative to some coordinate system, but this coordinate system may be moving relative to a second coordinate system.
where Object 2 can be anything from wind, moving water, train 12
Adding Vectors: Relative Motion
Define a coordinate system and determine
the vector components
Y
PT + TG = PG
T
PT = 2meters
P
.
θ
G
PTx=2m cosθ, PTy=2m sinθ
X
Table
φ
TG = 0.5meters
TGx=0.5m cos(360-φ), TGy=0.5m sin(360-φ)
Let’s assume the displacements occurred
simultaneously within a 2 second period .
We then rewrite the above vector
equations in terms of velocity.
Vpt+ Vtg=Vpg
cos(360-φ)=cos φ, sin(360-φ)=-sin φ
Vpt= cosθ (m/s) + sinθ (m/s)
Vtg= 0.25 cos φ (m/s) - 0.25 sin φ (m/s)
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Vpt= cosθ (m/s) + sinθ (m/s)
Vtg= 0.25 cos φ (m/s) - 0.25 sin φ (m/s)
Vpt+ Vtg=Vpg
Vpg= (0.25 cos φ + cosθ) (m/s)
+ (-0.25 sin φ + sinθ) (m/s)
Assume φ=60o,θ=45o
Vpg= 0.83 (m/s)
+ 0.49 (m/s)
|Vpg|= .
.
. m/s
Angle = tan-1(0.49/0.83)=30.6deg
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