King Fahd University of Petroleum

1
King Fahd University of Petroleum Minerals

• Mechanical Engineering
• Dynamics ME 201
• BY
• Dr. Meyassar N. Al-Haddad
• Lecture 2

2
Objective

• To introduce the concepts of position,
  displacement, velocity, and acceleration.
• To study particle motion along a straight line.

3
Rectilinear KinematicsSection 12.2

• Rectilinear Straight line motion
• Kinematics Study the geometry of the motion
  dealing with s, v, a.
• Rectilinear Kinematics To identify at any given
  instant, the particles position, velocity, and
  acceleration.
• (All objects such as rockets, projectiles, or
  vehicles will be considered as particles has
  negligible size and shape
• particles has mass but negligible size and
  shape

4
Position

• Position Location of a particle at any given
  instant with respect to the origin
• r Displacement ( Vector )
• s Distance ( Scalar )

5
Distance Displacement

• Displacement defined as the change in position.
• r Displacement ( 3 km )
• s Distance ( 8 km )
• Total length
• For straight-line
• Distance Displacement
• s r
• D s D r
• Vector is direction oriented
• Dr positive (left )
• Dr negative (right)

6
Velocity Speed

• Velocity Displacement per unit time
• Average velocity
• V Dr / Dt
• Speed Distance per unit time
• Average speed
• usp sT / Dt (Always positive scalar )
• Speed refers to the magnitude of velocity
• Average velocity
• uavg Ds / Dt

7
Velocity (con.)

• Instantaneous velocity
• For straight-line Dr Ds

8
Problem

• A particle moves along a straight line such that
  its position is defined by s (t3 3 t2 2 )
  m. Determine the velocity of the particle when t
  4 s.

At t 4 s, the velocity 3 (4)2 6(4) 24 m/s
9
Acceleration

• Acceleration The rate of change in velocity
  (m/s)/s
• Average acceleration
• Instantaneous acceleration
• If v gt v Acceleration
• If v lt v Deceleration

10
Problem

• A particle moves along a straight line such that
  its position is defined by s (t3 3 t2 2 )
  m. Determine the acceleration of the particle
  when t 4 s.
• At t 4

a(4) 6(4) - 6 18 m/s2
11
Problem

• A particle moves along a straight line such that
  its position is defined by s (t3 12 t2 36
  t -20 ) cm. Describe the motion of P during the
  time interval 0,9

t 0 2 4 6 9
s -20 12 -4 -20 61
v 36 0 -12 0 63
a -24 -12 0 12 30
Total time 9 seconds Total distance
(323281) 145 meter Displacement form -20 to
61 81 meter Average Velocity 81/9 9 m/s to
the right Speed 9 m/s Average speed 145/9
16.1 m/s Average acceleration 27/9 3 m/s2 to
the right
12
Relation involving s, v, and aNo time t
Position s
Velocity
Acceleration
13
Problem 12.18

• A car starts from rest and moves along a straight
  line with an acceleration of a ( 3 s -1/3 )
  m/s2. where s is in meters. Determine the cars
  acceleration when t 4 s.
• Rest t 0 , v 0

14
For constant accelerationa ac
15
Velocity as a Function of Time
16
Position as a Function of Time
17
velocity as a Function of Position
18
Free Fall

• Ali and Omar are standing at the top of a cliff
  of height H. Both throw a ball with initial
  speed v0, Ali straight down and Omar straight up.
  The speed of the balls when they hit the ground
  are vA and vO respectively. Which of the
  following is true
• (a) vA lt vO (b) vA vO (c) vA gt
  vO

v0
Omar
Ali
v0
H
vA
vO
19
Free fall

• Since the motion up and back down is symmetric,
  intuition should tell you that v v0
• We can prove that your intuition is correct

Equation
This looks just like Omar threw the ball down
with speed v0, sothe speed at the bottom
shouldbe the same as Alis ball.
Omar
v0
v v0
H
y 0
20
Free fall

• We can also just use the equation directly

Ali
same !!
Omar
v0
Ali
Omar
y H
v0
y 0
21
Summary

• Time dependent acceleration

• Constant acceleration

This applies to a freely falling object
22
Thank you
23
Gravity facts

• g does not depend on the nature of the material!
• Galileo (1564-1642) figured this out without
  fancy clocks rulers!
• Nominally, g 9.81 m/s2
• At the equator g 9.78 m/s2
• At the North pole g 9.83 m/s2
• More on gravity in a few lectures!