E102-MOTION ALONG A STRAIGHT LINE
GUIDE QUESTIONS:

1.From the data obtained, what is the effect of the height of the track to the cart’s acceleration? The data shows that sinӨ, which is dependent on the height, is getting higher as acceleration is increasing. This implicates that when object is at higher altitude, its acceleration is faster. 2.From the data obtained, how is time, t related to the inclination of the track? Explain why? Time and position of velocity are interrelated to each other and the height and gravitational pull affects the acceleration of a moving and a free falling object. 3.From the data obtained, how would you account the difference between the picket fence’s acceleration and the value of g? The value of the slope of a graph of average velocity versus time will be the acceleration due to gravity of the falling object.

E102-MOTION ALONG A STRAIGHT LINE

PROBLEM:
1.A police car is searching for a fugitive that managed to escape a while ago. Knowing that he is now safe, the fugitive begins to take a rest until he notices a police car approaching him at 10 m/s, accelerating at 5 m/s2 and it is 100 m away. The fugitive grabs a motorcycle and stars it accelerating at the same rate as the police car. How much time will it take the police car to catch the fugitive?

...Experiment 2: Kinematics of Human Motion
Abstract:
Kinematics is the branch of classical mechanics that describes the motion of bodies (objects) and systems (groups of objects) without consideration of the forces that cause the motion. There are four activities done in this experiment. Graphical analysis of human motion, where displacement vs time and velocity vs. time were graphed. Graphical analysis of motion where in the 10th seconds the total displacement is 18.75m, average velocity is 1.88m/s and instantaneous velocity is 3.76m/s. Reaction time where one of the normal reaction time among the group is 0.16s and the reaction time while someone is distracting the member is 0.30s, and lastly graph matching.
Introduction:
As a living organism, all of us have the potential to move, change in position, or go to different places. In short, life is in constant motion. From the prehistoric chase of antelopes across the savanna to the pursuit of satellites in space, mastery of motion has been critical to our survival and success as a species. The study of motion and of physical concepts such as force and mass is called Dynamics. Kinematics is one of the topics under dynamics. Kinematics describes motion without regard to its causes. In this experiment, kinematics focuses in one dimension: a motion along a straight line. This kind of motion, actually...

...Physics 12 – Kinematics Worksheet
1. Which one of the following contains only vector quantities?
A. mass, time
B. force, velocity
C. time, momentum
D. acceleration, speed
2. An airplane heads due north with an airspeed of 75 m/s. The wind is blowing due west at 18 m/s. What is the airplane’s speed relative to the ground?
A. 57 m/s
B. 73 m/s
C. 77 m/s
D. 93 m/s
3. Two velocity vectors, v1 and v2 are shown.
Which of the following best represents the resultant of the addition of the two velocity vectors?
4. A car travelling north at 20 m/s is later travelling west at 30 m/s. What is the direction of the change in velocity?
5. Two forces act at a single point as shown.
What is the magnitude of the resulting force?
A. 15 N
B. 22 N
C. 27 N
D. 30 N
6. A boat shown below travels at 4.2 m/s relative to the water, in a river flowing at 2.8 m/s.
At what angle must the boat head to reach the destination directly across the river?
A. 34o
B. 42o
C. 48o
D. 56o
7. In landing, a jet plane decelerates uniformly and comes to a stop in 38 s, covering a distance of 1500 m along the runway. What was the jet’s landing speed when it first touched the runway?
A. 2.1 m/s
B. 39 m/s
C. 79 m/s
D. 170 m/s
8. A 35 kg object released from rest near the surface of a planet falls 7.3 m in 1.5 s. What is the
acceleration due to gravity on this planet?
A. 4.9 m/s2
B. 6.5 m/s2...

...Kinematics
Position
To specify a position vector you need to specify:
• Origin
• Distance
• Direction
If using a 3D right-handed coordinate system with the
origin being the reference point for the position vector,
it is enough to specify the coordinates x, y and z.
For a moving object the position vector is a function of
time.
Velocity & Acceleration
• Velocity is defined as the change in position over
a change in time; thus the averagevelocity is
and the instantaneous velocity is
• For motion in one dimension the velocity is the
slope of the position line plotted versus time.
• The same logic is used in deriving the average and
instantaneous acceleration resulting in:
• Jerk is defined as the rate of change of
acceleration:
Example 1
• A body starts from rest at x=0. ax(t)=2t-4 [m/s2].
Find the jerk and the position as a function of
time.
Solution:
At rest =>vx0=0; At x=0 =>x0=0
Integrating:
vx(t)=vx0+t2-4t=t2-4t [m/s]
x(t)=x0+(t3/3)-2t2=(t3/3)-2t2 [m];
jx=dax/dt=2 [m/s3]
Example 2
A body is moving along x
with a constant jerk. At
t=2s, its velocity is 4
m/s. At t=4.5s and
t=5s, its acceleration is
respectively 2.1 m/s2
and 4m/s2. At t=1s it is
at x=3.4m. Determine
the position of the
body at t=7s.
Example 2
Example 3
A body is launched with
an initial speed of
50m/s at an angle of
60 degrees with the
horizontal from a
height of 2m. How
far from its initial...

...projectile’s motion compare with the motion of
vertical free fall when air resistance is negligible?
1. Less than that of free fall
2. Greater than that of free fall
3. Identical to that of free fall
1
the ground depends on v0 .
3. The ball is freely falling with acceleration
g, from the instant it is released until it strikes
the ground.
4. The time it takes for the ball to hit the
ground depends on v0 , g and h.
004 10.0 points
The velocity of a projectile at launch has a
horizontal component vh and a vertical component vv . When the projectile is at the highest point of its trajectory, identify the vertical
and the horizontal components of its velocity
and the vertical component of its acceleration.
Consider air resistance to be negligible.
4. It cannot be determined.
002 10.0 points
A heavy crate accidentally falls from a highﬂying airplane just as it ﬂies directly above a
shiny red Camaro parked in a parking lot.
Relative to the Camaro, where will the
crate crash?
Vertical
Velocity
Horizontal
Velocity
Vertical
Acceleration
1.
vv
vh
0
2.
vv
0
0
3.
0
vh
0
4.
0
0
g
5.
0
vh
g
1. The crate will hit the Camaro.
2. The crate will continue to ﬂy and will not
crash.
3. The crate will not hit the Camaro, but
will crash a distance beyond it determined by
the height and speed of the plane.
4. The crate will hit the...

...[pic]
a What was the distance of the race?
(1)
b How long did it take the runner to complete the race?
(1)
c For how long did the runner rest during the race?
(1)
d Between which two points was the runner moving the fastest?
Give a reason for your answer.
(2)
e Between which two points did the runner travel at the same speed as they did between A and B?
(1)
f Calculate the speed of the runner between B and C in metres per second.
Show clearly how you work out your answer.
(3)
3 A cyclist is travelling along a straight road. The graph shows how the velocity changes with time for part of the journey.
[pic]
a Explain how is acceleration found from a velocity–time graph.
(1)
b Copy and complete the following sentences using the list of words and phrases below. Each one can be used once, more than once or not at all.
is stationary travels at a constant speed accelerates decelerates
i Between A and B the cyclist …………………… (1)
ii Between B and C the cyclist …………………… (1)
iii Between C and D the cyclist …………………… (1)
c i Use the graph to find the maximum speed of the cyclist.
(2)
ii Use the graph to find the distance travelled in metres between 4 and
8 seconds. Show clearly how you work out your...

...Exercises for Chapter 1 Kinematics
1. An impulsive retarding force of 3 seconds duration acts on a particle which is moving with a forward velocity of 60 m/s. The oscilloscope record of the deceleration is shown. Determine the approximate velocity of the particle at t = 9 s. [answer: -58 m/s] 2. A car can decelerate at 0.8 ‘g’ on a certain road. Find the total emergency stopping distance measured from the point where the driver first sights the danger for a speed of 100 km/hr. The time taken for the driver to identify the hazard, decide on a course of action, and apply the brakes is 0.75 s. [Answer: 70 m] 3. An underground train on the Mass Transit Railway moves away from a station with an initial acceleration of 0.9 m/s2. The acceleration decreases uniformly with time until after half a minute it is 0.3 m/s2. Calculate the speed reached and the distance travelled during this time. [Answer: 18 m/s, 315 m] 4. The magnitude of the acceleration and deceleration of an express lift is limited to 0.4 ‘g’, and the maximum vertical speed is 400 m/min. Calculate the minimum time required for the lift to go from rest at the 10th floor to a stop at the 30th floor, a distance of 100 m. [Answer: 16.7 s] 5. A cam rotates at 500 rev/min and imparts ‘parabolic’ motion (i.e. Constant acceleration and deceleration) to a reciprocating follower. The total lift of the follower is 20 mm and this takes place during 90 degrees of cam rotation.
If the...

...-springRobust control applied to a cart-spring pendulum system with uncertainty
Dan Dai Advisor: Professor Roy Smith University of California, Santa Barbara
II. ROBUST C ONTROL STATEMENT The objective of this project is to design a controller that meets the speciﬁed robust performance criteria. When the cart-spring pendulum system is considered, these criteria reﬂects on robustness to outside disturbance and plant uncertainty. To get this controller, it is necessary to set up this problem in a very systematic way. The cart-spring pendulum system is a complex system and it has a few important properties to study. For the purpose of deriving a model, the experimental system will be considered to be composed of a massless spring attached to a frictionless cart from which a slender rod freely hangs. The output of the system is the position p of the cart, in meters, relative to the spring’s equilibrium point and the angular position θ of the pendulum, in radians, relative to the vertical; both positions are measured with optical encoders. The physical inputs of the system are the voltage u applied to the armature of the dc motor, in Volts, and a disturbance force w, in Newtons. The operating range of D/A converter, is [-5,5] Volts. The disturbance w is a force in the plane of motion orthogonal to the pendulum of length 2l and acts at a disturbance of (4/3)l from the cart-pendulum hinge. A...

...Problems (Chapter 3)
Review Example problems #1 - 12 by yourself.
Problem 3 (page 96): A web page designer creates an animation in which a dot on a computer screen has a position of r = [4 cm + (2.5 cm/s2)t2]i + (5 cm/s)t j.
a) Find the magnitude and direction of the dot’s average velocity between t = 0 and t = 2 s.
b) Find the magnitude and direction of the instantaneous velocity at t = 0, t = 1 s, nd t = 2 s.
c) Sketch the dot’s trajectory from t = 0 to t = 2 s, and show the velocities calculated in part (b).
(a) Identify and Set Up: From [pic] we can calculate x and y for any t.
Then use Eq. (3.2), in component form.
Execute: [pic]
At [pic] [pic]
At [pic] [pic]
[pic]
[pic]
| |[pic] | |[pic] |
| | | |[pic] |
| | | |[pic] |
|Figure 3.3a | | |
Evaluate: Both x and y increase, so [pic] is in the 1st quadrant.
(b) Identify and Set Up: Calculate [pic] by taking the time derivative of [pic]
Execute: [pic]
[pic] [pic] [pic] [pic] and [pic]
[pic] [pic] [pic]...

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