Chapter 6: Motion in a Plane
1
Position and Velocity in 2-D
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Displacement
Velocity
Average velocity
Instantaneous
velocity
Instantaneous
acceleration
Average acceleration
2
Directions of Instantaneous and
average velocities
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Instantaneous
velocity at any point
on the curve is along
the tangent drawn at
that point
Average velocity
points in the direction
of the displacement
vector
3
Components of velocity
4
Acceleration (Instantaneous and
Average)
5
Equations of Motion in 2-D
6
If a particle’s motion is
governed by x=2t2 and y=5t
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At any time
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What would be its displacement, velocity, and
acceleration?
What would be its speed?
What is the angle of inclination?
At t = 5 s
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What would be its position, velocity, and acceleration?
Calculate its speed
Calculate its angle of inclination θ
7
Projectile Motion
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A projectile is an
object that moves in
2-D under the
influence of only the
gravitational force
For projectiles, ax=0
and ay=-g
8
Components of velocity and
acceleration of a Projectile
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A projectile is launched
with an initial velocity
(9.8,19.6) m/s
Observe that the xcomponent of velocity is
not changing (no change
in the length or direction)
Vertical component of
the velocity is changing
in length and direction
due to gravitational
force!
9
Dynamics of a projectile
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Projectile motion is made up of two
independent motions
Uniform motion with constant velocity along
x- direction (horizontal)
Free-fall motion in the vertical direction
10
Range of a Projectile
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Range is the longest
horizontal distance
traveled by a projectile
What should be θ for
the projectile to have
longest range?
When would the
projectile reach
maximum height?
11
Projectile Motion as a function
of θ
12