Motion
The study of kinematics is often
referred to as the "geometry of
motion".
• To describe motion, kinematics studies the
trajectories of points, lines and other
geometric objects and their differential
properties such as velocity and acceleration
• The study of motion is fundamental to
the principles of physics, and it is
applied to a wide range of topic, such
as automotive engineering, rocket
launches, and improvement in athletic
performances (kinesiology)
As we saw with the RoadRunner lab…
f(x) = model of displacement vs time
f’(x) = velocity
f’’(x) = acceleration
f’’’(x) = called “jerk” or “jolt”
f’’’’(x) = called “jounce”
Anything beyond are called “hyperjerk” systems.
• As an everyday example, driving in a car
can show effects of acceleration and jerk.
The more experienced drivers accelerate
smoothly, but beginners provide a jerky
ride.
Changing gears, especially with a footoperated clutch, offers well-known examples:
although the accelerating force is bounded by
the engine power, an inexperienced driver
lets you experience severe jerk, because of
intermittent force closure over the clutch
A construction
worker drops a
hammer from a
height of 90m
towards the
ground
The height of the hammer, as a function of
time, is described by h(t) = 90 – 4.9t2
1.Determine the first derivative h’(t),
What does it mean?
2.Determine the second derivative
h’’(t), what does it mean?
3. When will the hammer hit the
ground?
4. Determine the impact velocity
of the hammer?
Velocity and Acceleration have
directions….
If the acceleration and the velocity of an
object have the same sign at a particular
time, then the object is being pushed in
the direction of the motion, and the object
is speeding up.
If the acceleration and the velocity of an
object have opposite signs at a particular
time, then the object is being pushed in
the opposite direction of its motion, and
the object is slowing down.
Velocity and Acceleration have
directions….
An object is speeding up, at time t if
v(t) X a(t) > 0
An object is slowing down, at time t if
v(t) X a(t) < 0
Read ex 3 on
page 103
Pg 106
[1-4] a,c
5a,b, 8, 9,10,13