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3Material AICLE 4º de ESO: Physics of motion (Solucionario)
TEACHER´S KEY
A.1.a. During the intervals A and Db. During the interval Cc. During the interval Bd. No there wasn’t a negative position as you can see in the graph, the position isn’t negative.e. During the interval C.f. This type of graphs never shows the trajectory, we only know the trajectory if we can see the path that the person follows.
A.2. Questions: a. It’s in Andújar, where the journey startsb. No, the position is a vector. On the map we can draw vectors, but we need the map scale.c. The trajectory can be drawn on the map.d. The route information contains data of time and distances including.e. Of course no, because we haven’t got data about position.f. Of course. Have a look at the next graph.Using a Spreadsheet (Excel), we can obtain the graphs:
t (min) Distance (km)
0,00 0,00
34,00 37,80
35,00 39,00
36,00 39,40
41,00 44,70
A la vueltat (min) Distance (km)
0,00 0,00
5,00 5,30
6,00 5,70
8,00 6,90
41,00 44,70
4 Material AICLE 4º de ESO: Physics of motion (Solucionario)
A.4. Listening. Se reproduce el texto completo marcando en rojo las palabras que son los huecos en la actividad:
Distance and DisplacementDistance is a scalar quantity representing the interval between two points. It is just the magnitude of the interval. However, displacement is a vector quantity and can be defined by using the concept of distance. It can be defined as distance between the initial position and final position of an object. It must be the shortest interval connecting the initial and final positions, which is a straight line. Let’s look at the below example for deep understanding.
Look at the picture on the left, a boy travels from D to A, A to B, B to C and C to D. Displacement from D to D (which are our initial and final positions) is zero. However, distance travelled is not zero. It is equal to the perimeter of the rectangle.
Another example of distance and displacement is illustrated in figure on the right.The person walks from the point A to B to C.
What distance does he travel?
What is the displacement?
Let’s calculate first the distance that person travels. While calculating distance, we look at the numeric value of interval between travelled positions. As you can see from figure he travels from A to B to C: Distance from A to B is 4 m and B to C is 3 m. Their sum will give us total distance; 4+3=7
Then it’s time to calculate displacement. Displacement is a vector quantity. Thus, it must have both magnitude and direction. In this example our initial position is A and our final position is C. Displacement vector is an interval between the initial and final positions. As it clearly seen in the figure interval between A to C is 5 m. So, our displacement vector is 5m and its direction is from the point A to C.
Questions:
1. True or false. Why?.a) This is false, distance is a scalar quantity while displacement is a vector.b) This is true. They have in common the magnitude.c) False. The distance is the length of the circuit.d) True.e) False. Positions initial and final are only necessary.
5Material AICLE 4º de ESO: Physics of motion (Solucionario)
2. Draw a circumferential with a radius of 5 cm. a) i) The length of two circumferential: 2*2π*5 cmii) Displacement is 0
b) i) 3π* 5 cm.ii) If the lap starts at 0º then the displacement is 5 cm west.
A.6. Text comprehension.1. Conclusions: Complete the sentences:
a) Speed is a quantity that states the distance travelled in each time unit.b) Velocity is a quantity that states the displacement produced in each time unit.c) The formulae above indicate average. Instantaneous velocity shows the velocity at one point.
2. Simple exercises.a) Average speed = 3.3 m/sb) Average speed = 8 m/sc) Interval 1: 4.53 cm/s. Interval 2: 8.98 cm/s A.8.
Model Name 0-100 km/h time (s) Acceleration m/s2
Bugatti Veyron 2.5 11.11
Ariel Atom 2.8 9.92
Porsche 911 Turbo S 2.9 9.58
Ferrari 458 3.2 8.68
Nissan GT-R 3.3 8.42
Jaguar XJ2220 3.5 7.94
6 Material AICLE 4º de ESO: Physics of motion (Solucionario)
A.91) Find the words on the right.
Se reproduce el texto íntegro señalando en rojo las palabras de los huecos.
How does a radar detect the speed of a vehicle?
A radar uses electromagnetic waves to detect objects and provide information about them (distance, speed...).The radar sends radio waves (electromagnetic waves) at a given frequency and listens for their return (echo). If an object is in the beam, some waves will bounce off it and return to the radar. By dividing the time it took for the waves to travel back and forth by the speed of the waves (the speed of light) it is then easy to determine the distance.
To determine speed, radars use the doppler effect. They measure and scale the frequency variation between the radio wave sent and the radio wave received (echo). If the object is moving away, the frequency will be lower, if it is getting closer, the frequency will be higher. Depending on how much lower or higher the echo frequency is, it is possible to know at what speed the object is moving from the radar position. This technology is now quite old and easy to jam.
A newer system called LIDAR (light detection and ranging) does not use the Doppler Effect. It only does calculate the distance at which the object is, but does so very often. From the change in distance observed in a given lapse of time it is simple to extrapolate the speed. The frequencies used by Lidar are higher (laser lights) and more difficult to jam. To be even more jam-proof, some systems use various frequencies, making jamming systems more complex and expensive. This Lidar system is now extensively used in the new police speed detection equipments.
7Material AICLE 4º de ESO: Physics of motion (Solucionario)
Questions:
1. The frame of reference is in the position where the device is installed.2. A very short time lapse because these waves travel with a high speed.3. They use electromagnetic waves (radio waves)4. This device works with very high frequency waves: LASER5. Open response6. Open response. Read data in the DGT web can be a good idea.7. If you look for information can discover that this type of waves need metal surface to work correctly.
A.101. The meaning of this acceleration is that the rate of variation of the velocity with respect the time is 1 m/s each second.
Given that:
Let assume that t0 = 0
Then V = V0 + a t.
Using this formula we can complete the chart:
t (s) 0 2 4 6 8 10
V (m/s) 2 4 6 8 10 12
Drawing the graphIn order to calculate the distance covered we can follow two ways:
• Calculate the area under the graph.
• Use the equation for this type of motion:
Distance= V0.t + ½ a t2Distance= 2 m/s . 10 s. + ½ 1 m/s2 .102 s2Distance= 70 m.
0
24
68
1012
14
0 5 10 15
Time (s)
V (m
/s)
8 Material AICLE 4º de ESO: Physics of motion (Solucionario)
A.11.Se reproduce el texto completo con las palabras perdidas marcadas en rojo.
Galileo’s Leaning Tower of Pisa experiment
Vivani’s early biography of Galileo informs us of the story that Galileo dropped two objects of different mass from the top of the Leaning Tower of Pisa. He did so as an experiment to disprove Aristotle’s theory of gravity, which states that objects fall at a speed relative to their mass. It is generally accepted that this is not a true story, but rather a fictional tale passed down among other scientific folklore.
However Galileo did a simple bit of reasoning to rebut Aristotle, which is said to be one of the earliest and simplest recorded thought experiments.
Galileo reasoned as follows:Imagine two objects, one light and one heavier than the other one, are connected to each other by a string. Drop this system of objects from the top of a tower. If we assume heavier objects do indeed fall faster than lighter ones (and conversely, lighter objects fall slower), the string will soon pull taut as the lighter object retards the fall of the heavier object. But the system considered as a whole is heavier than the heavy object alone and therefore should fall faster. This contradiction leads one to conclude the assumption is false.
Questions:
• As you can conclude Galileo was right.• Free response.• The free fall speed doesn’t depend in the mass of the object.• There is an important variable that is the friction with air.
A.12
Across3. VELOCITY4. RELATIVE7. MOTION
Down1. POSITION2. ACCELERATION5. REFERENCE6. TIME
9Material AICLE 4º de ESO: Physics of motion (Solucionario)
Una propuesta de mapa conceptual es;
