1The table gives values of distance and time for a child travelling along a straight track competing in an egg and spoon race. Time (seconds) 0 5 10 15 20 25  Distance (metres) 0 8 20 20 24 40  aCopy the graph axes below on to graph paper. Plot a graph of distance against time for the child. [pic](3)
bName the dependent variable shown on the graph.
(1)
cWhat type of variable is this?
(1)
dUse your graph to estimate the distance travelled in 22 seconds.
(1)
eUse your graph to estimate the time taken for the child to travel 15 metres.
(1)
fDescribe the motion of the child between 10 seconds and 15 seconds. Give a reason for your answer.
(2)
2The graph shows how far a runner travels during a charity running race. [pic]
aWhat was the distance of the race?
(1)
bHow long did it take the runner to complete the race?
(1)
cFor how long did the runner rest during the race?
(1)
dBetween which two points was the runner moving the fastest? Give a reason for your answer.
(2)
eBetween which two points did the runner travel at the same speed as they did between A and B?
(1)
fCalculate the speed of the runner between B and C in metres per second. Show clearly how you work out your answer.
(3)
3A cyclist is travelling along a straight road. The graph shows how the velocity changes with time for part of the journey. [pic]
aExplain how is acceleration found from a velocity–time graph.
(1)
bCopy 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
...Kinematics
Position
To specify a position vector you need to specify:
• Origin
• Distance
• Direction
If using a 3D righthanded 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 average velocity 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)=2t4 [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+t24t=t24t [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
position will it land?
What will be the
angle it makes with
the horizontal when
hitting...
...LAB # 1
Graph Matching
Principles of Physics I Laboratory
Breanna Wilhite
Introduction
In this lab motion will be represented by graphs that plots distance and velocity vs. time. A motion detector will be used to measure the time it takes for a high frequency sound pulse to travel from the detector to an object and back. By using this method sound can determine the distance to the object, or its position. This device will determine in what direction the woman in the video was walking and how fast she was walking. This information will be plotted on a graph and show the motion as the woman moves, whether she speed up or slowed down. Logger Pro will use the change in position to calculate the object’s velocity and acceleration. All of this information is in graph form. A qualitative analysis of the graphs of motion will help you develop an understanding of the concepts of kinematics.
Theory
The motion of an object can be measured using a motion detector. The detector helps in knowing where an object is according to an indication point. How fast and in what direction an object is moving, and how an object is accelerating is necessary in understanding the kinematicsgraphs.
The Motion detector uses pulses of ultrasound that bounces off of an object to determine the position of the person/object. As the person moves, the change in its position is...
...Angular Kinematics
An object on a point that rotate a fixed axis has circular motion around the same axis. Linear quantities cannot be used for circular motion. This is due to the extended objects rotational motion rather that a particles linear motion. Circular motion, for this reason, is described in terms of the change in angular position. Except for the points on the axis, all the points on a rotating rigid object during any time interval move through the same angle.
Many equations describing circular motion require angles to be measured in radians (rad) instead of degrees. Any angle θ measured in radians, in general, is defined by the equation. If the arc length, s, and the length of the radius, r, is equal, the angle θ swept by r is equal to one radian. The units cancel and the abbreviation radian is substituted because θ is the ratio of the length of the radius (distance) to an arc length (also a distance). In other words, the radian is a pure number, with no dimensions.
When the light on a Ferris wheel moves one revolution of the wheel (angle of 360˚) the circumference of a circle, which is r, is equal to the arc length s. By substituting this value for s (into the equation above) gives the corresponding angle in radians . Hence radians equals 360˚, or one complete revolution. An angle approximately 2(3.14) =6.28 radians corresponds with one revolution. Figure 1 to the right is a circle that is marked with both degrees and radians.
Any angle...
... 1. PIE CHART
This pie chart shows Mark’s monthly budget. The highest designation of his budget will go to his foods with 45% of his total allowance. Next is for lodging with 30% followed by the projects and fare which will have 10%. The least designation for his budget will be for his savings which has 5% only.
2. BAR GRAPH
The bar graph shows the yearly tourist count for the provinces of region V. the province of Albay got the highest number of tourist with 450 000. It is followed by the provinces of Camarines Sur and Camarines Norte with 400 000 and 350 000 respectively. Sorsogon got 300 000 and Catanduanes with 250 000. The province of Masbate got the lowest number of tourist with 200 000.
3. LINE CHART
Here is a line chart for the number of absentees in class of Mr. Lozada for the 1st semester in 4 of her subjects. English has the most number of absents with 5 meetings. It is then followed by Math and Science with 4 and 3 meeting respectively while Filipino has the least absentees with only 2 meetings.
4. TABLES
KLINE DORMITORY SPORTS EQUIPMENT SPORT  NUMBER OF EQUIPMENT 
VOLLEYBALL  7 
BADMINTON  7 
SOCCER  4 
BASEBALL  12 

This table shows the number of sport equipment for each of the favorite sport of the KLINE scholars. The dormitory has the most sufficient sport equipment with 12. And Soccer is the sport with less number of equipment with only 4 sport equipment.
5.
PICTOGRAPH
MEMBERS’ SAVINGS...
... 
Male 57 59% 
Female 40 41% 
Total 97 100% 
Table 1 reveals the sex profile of the respondents. As reflected on the table, the male has the larger percentage than the female. Out of 97 respondents, 57 or 59% are male while 40 or 41% are female.
To illustrate visually the sex profile, the graph is presented below.
20
Graph 1
[pic]
Gender Profile of the Respondents
Table 2
Analytical Skills
Respondents  S N Computed t Tabular t Decision Remark 
Male 10.84 2.95 57     
    0.33 1.9852 Accept Ho Significant 
5% level of significant and 26 degrees of freedom
Table 2 reveals the level of significant and the degrees of freedom. As reflected on...
...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.
E102MOTION 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?
x = xo + vot + 1at2
2
xpolice = 0m +10m/s (t) + 0.5(5m/s2)t2
xfugitive = 100m +0m/s (t) + 0.5(5m/s2)t2...
...DistanceTime Graphs
Constructing graphs of an objects motion gives a better idea of the behaviour of the moving object.
A distancetime graph is constructed by having the distance as the vertical axis and the time as the horizontal axis. By recording the distance travelled over different intervals of time and plotting these values a distancetime graph can be plotted. From this plot information about the moving object can easily be extracted.
This animation shows a distancetime graph:
Points to remember
In a distancetime graph;
* The average speed can be determined from the slope/gradient of the graph.
* The steeper the gradient the higher the average speed.
* A horizontal line indicates the object is stationary (not moving).

VelocityTime Graphs
A velocitytime graph is constructed by having the velocity as the vertical axis and the time as the horizontal axis. By recording the velocity over different intervals of time and plotting these values a velocitytime graph can be plotted. From this plot information about the moving object can easily be extracted.
The animation below shows a velocitytime graph.
Points to remember
In a velocitytime graph:
* The acceleration can be determined from the slope/gradient of the...
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