# Chapter-3 Kinematics in Two Dimensions

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```					         Chapter-3
Kinematics in Two Dimensions
3.1 Displacement, Velocity,
and Acceleration
Displacement

ro  initial position

r  final position

  
r  r  ro  displaceme nt
Average Velocity

Average velocity is the
displacement divided by
the elapsed time.

        
 r  ro r
v        
t  to   t
Instantaneous Velocity
The instantaneous velocity indicates how fast
the car moves and the direction of motion at each
instant of time.


         r
v  lim
t 0 t
Acceleration

Average acceleration:

Instantaneous acceleration:
Men's 800m Race
A race finishes at the same place as it
started. The contestants start from rest
and cross the finish line running. What
can you say about the average speed,
the average velocity, and the average
acceleration?
Men's 800m Race
A race finishes at the same place as it
started. The contestants start from rest
and cross the finish line running. What
can you say about the average speed,
the average velocity, and the average
acceleration?

Answer: average speed # 0 m/s, average velocity = 0 m/s, average acceleration # 0 m/s2
3.2 Equations of Kinematics
in Two Dimensions
Kinematic equations for a one dimensional motion with constant
acceleration are,
a) v = v0 + at
b) x = ½(v0 + v)t
c) x = v0 t + ½at2
d) v2 = v02 + 2ax ;
x = distance, a = acceleration, v = final velocity, v0 = initial
velocity, t = travel time.
Kinematics Equations
3.3 Projectile Motion
3.3 Projectile Motion

Assumptions:
1. Air resistance is neglected
2. Gravity is constant, 9.8 m/s2, down.
Velocity of the football
A Falling Care Package
An airplane moving horizontally with a constant velocity of +115
m/s at an altitude of 1050 m. The plane releases a “care package”
that falls to the ground along a curved trajectory.
Velocity of the care package
Demonstration
Conceptual Example 4

Suppose you are driving in a convertible with the top down. The car is
moving to the right at a constant velocity. As Figure 3.11 illustrates,
you point a rifle straight upward and fire it. In the absence of air
resistance, where would the bullet land—behind you, ahead of you, or
in the barrel of the rifle?
Playing Shortstop
A player picks up a ground ball and throws it horizontally with a
speed of 24 m/s. It is caught after 0.42 s later at point B.
a. How far apart are the two players?
b. What is the distance of vertical drop, AB?

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 views: 6 posted: 12/14/2011 language: English pages: 18
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