In this chapter we will learn about the motion of objects. But first we will consider objects at rest.
■ The most important property concerning an object at rest, is it's position. We must be able to say 'where' that object is.
For that, we use references. Let us see some examples:
• Consider fig.1.1(a) below. The school is situated 2 km north of the railway station. Here, the railway station is used as the reference to specify the position of the school
• In fig.1.1(b), a car is parked 15 m to the left of the house. Here, the house is used as the reference to specify the position of the car.
■ With out a reference, we will not be able to tell the position of an object.
The object is displaced from O to B. The distance OB is 5 m. So the displacement of the object is 5m.
6. Note that the object travelled a total distance of 7 m. But it's displacement is only 5 m.
7. The line OB makes an angle of 30o with the horizontal X axis.
■ So we are able to specify the final position of the object. We do that as follows:
• The displacement of the object is 5 m
• This 5 m is along a line which makes an angle 30o with the horizontal axis
8. Thus we see that, to specify a position of the object, we need two items:
(i) The magnitude of the displacement
♦ In our present case, it is '5m'.
(ii) The direction of the displacement
♦ In our present case, it is 'a line making 30o with the horizontal'.
■ 'Magnitude of the displacement' is the 'shortest distance measured from the initial to the final position of an object'.
9. Note that, if instead of stopping at B, the object travels back to O along OB, the distance travelled will be 4+ 3 + 5 = 12 m. And the displacement will be zero.
Another example:
1. Consider fig.1.2(b) above. An object is initially at rest at the origin point 'O'.
The object is displaced from O to R. The distance OR is 4.8 m. So the displacement of the object is 4.8 m.
6. Note that the object travelled a total distance of 16 m. But it's displacement is only 4.8 m.
7. The line OR makes an angle of 44o with the horizontal X axis.
■ So we are able to specify the final position of the object. We do that as follows:
• The displacement of the object is 4.8 m
• This 4.8 m is along a line which makes an angle 44o with the horizontal axis
8. Thus, as in the prvious example, here also we see that, to specify a position of the object, we need two items:
(i) The magnitude of the displacement
♦ In our present case, it is '4.8m'.
(ii) The direction of the displacement
♦ In our present case, it is 'a line making 44o with the horizontal'.
■ 'Magnitude of the displacement' is the 'shortest distance measured from the initial to the final position of an object'.
9. Note that, if instead of stopping at R, the object travels back to O along OR, the distance travelled will be 7+ 4 + 5 + 4.8 = 20.8 m. And the displacement will be zero.
In the next section, we will see Uniform and Non-uniform motion.
■ The most important property concerning an object at rest, is it's position. We must be able to say 'where' that object is.
For that, we use references. Let us see some examples:
• Consider fig.1.1(a) below. The school is situated 2 km north of the railway station. Here, the railway station is used as the reference to specify the position of the school
 |
| Fig.1.1 |
■ With out a reference, we will not be able to tell the position of an object.
Now let us see objects in motion.
1. Consider fig.1.2(a) below. An object is initially at rest at the origin point 'O'.
 |
| Fig.1.2 |
2. From O, it travels in the positive direction of the x-axis for a distance of 4 m, and reaches 'A'.
3. Then it travels in the positive direction of the y-axis for a distance of 3 m, and reaches 'B'.
4. So B is the final position of the object. The object travelled a total distance of 3 + 4 = 7 m and reached B.
5. We can say this:The object is displaced from O to B. The distance OB is 5 m. So the displacement of the object is 5m.
6. Note that the object travelled a total distance of 7 m. But it's displacement is only 5 m.
7. The line OB makes an angle of 30o with the horizontal X axis.
■ So we are able to specify the final position of the object. We do that as follows:
• The displacement of the object is 5 m
• This 5 m is along a line which makes an angle 30o with the horizontal axis
8. Thus we see that, to specify a position of the object, we need two items:
(i) The magnitude of the displacement
♦ In our present case, it is '5m'.
(ii) The direction of the displacement
♦ In our present case, it is 'a line making 30o with the horizontal'.
■ 'Magnitude of the displacement' is the 'shortest distance measured from the initial to the final position of an object'.
9. Note that, if instead of stopping at B, the object travels back to O along OB, the distance travelled will be 4+ 3 + 5 = 12 m. And the displacement will be zero.
1. Consider fig.1.2(b) above. An object is initially at rest at the origin point 'O'.
2. From O, it travels a distance of 7 m, and reaches 'P'. Then it travels 4 m and reaches 'Q'. Finally it travels 5 m and reaches 'R'.
3. So R is the final position of the object. The object travelled a total distance of 7 + 4 + 5 = 16 m and reached R.
5. We can say this:The object is displaced from O to R. The distance OR is 4.8 m. So the displacement of the object is 4.8 m.
6. Note that the object travelled a total distance of 16 m. But it's displacement is only 4.8 m.
7. The line OR makes an angle of 44o with the horizontal X axis.
■ So we are able to specify the final position of the object. We do that as follows:
• The displacement of the object is 4.8 m
• This 4.8 m is along a line which makes an angle 44o with the horizontal axis
8. Thus, as in the prvious example, here also we see that, to specify a position of the object, we need two items:
(i) The magnitude of the displacement
♦ In our present case, it is '4.8m'.
(ii) The direction of the displacement
♦ In our present case, it is 'a line making 44o with the horizontal'.
■ 'Magnitude of the displacement' is the 'shortest distance measured from the initial to the final position of an object'.
9. Note that, if instead of stopping at R, the object travels back to O along OR, the distance travelled will be 7+ 4 + 5 + 4.8 = 20.8 m. And the displacement will be zero.
A special case:
1. Consider fig.1.3 below. An object is initially at rest at the origin point 'O'.
2. From O, it travels in the positive direction of the x-axis for a distance of 40 m, and reaches 'A'.
The object is displaced from O to C. The distance OC is 20 m. So the displacement of the object is 20 m.
7. Note that the object travelled a total distance of 120 m. But it's displacement is only 20 m.
8. The line OC makes an angle of 0o with the horizontal X axis.
■ So we are able to specify the final position of the object. We do that as follows:
• The displacement of the object is 20 m
• This 20 m is along a line which makes an angle 0o with the horizontal axis
9. Thus, here also we see that, to specify a position of the object, we need two items:
(i) The magnitude of the displacement
♦ In our present case, it is '20 m'.
(ii) The direction of the displacement
♦ In our present case, it is 'a line making 0o with the horizontal'.
■ 'Magnitude of the displacement' is the 'shortest distance measured from the initial to the final position of an object'.
10. Note that, if instead of stopping at B, the object travels back to O along OC, the distance travelled will be 40 + 30 + 50 +20 = 140 m. And the displacement will be zero.
11. In this example, the direction of the displacement makes zero angle with the x-axis. This is because, all the travels were made along the x-axis. The object never left the x-axis.
12. A very interesting result:
• Let us take all the distances travelled towards the right (that is., positive direction of the x-axis) as positive
• And all the distances travelled towards left (that is., negative direction of the x-axis) as negative
• Now we add the distances:
OA + AB + BC = 40 + 30 -50 = 20
• '20' is the magnitude of the final displacement
From the discussion so far in this chapter, we can write this:
■ To specify the position of an object, we need two items:
• Magnitude of the displacement
• Direction of the displacement
1. Consider fig.1.3 below. An object is initially at rest at the origin point 'O'.
 |
| Fig.1.3 |
3. Then it travels in the same direction for a distance of 30 m, and reaches 'B'.
4. From B, it travels in the opposite direction. That is in the negative direction of the x-axis. In this direction, it travels for a distance of 50 m, and reaches 'C'. This travel is indicated by the top most line between B and C in the fig.1.3
4. From B, it travels in the opposite direction. That is in the negative direction of the x-axis. In this direction, it travels for a distance of 50 m, and reaches 'C'. This travel is indicated by the top most line between B and C in the fig.1.3
5. So C is the final position of the object. The object travelled a total distance of 40 + 30 + 50 = 120 m and reached C.
6. We can say this:The object is displaced from O to C. The distance OC is 20 m. So the displacement of the object is 20 m.
7. Note that the object travelled a total distance of 120 m. But it's displacement is only 20 m.
8. The line OC makes an angle of 0o with the horizontal X axis.
■ So we are able to specify the final position of the object. We do that as follows:
• The displacement of the object is 20 m
• This 20 m is along a line which makes an angle 0o with the horizontal axis
9. Thus, here also we see that, to specify a position of the object, we need two items:
(i) The magnitude of the displacement
♦ In our present case, it is '20 m'.
(ii) The direction of the displacement
♦ In our present case, it is 'a line making 0o with the horizontal'.
■ 'Magnitude of the displacement' is the 'shortest distance measured from the initial to the final position of an object'.
10. Note that, if instead of stopping at B, the object travels back to O along OC, the distance travelled will be 40 + 30 + 50 +20 = 140 m. And the displacement will be zero.
11. In this example, the direction of the displacement makes zero angle with the x-axis. This is because, all the travels were made along the x-axis. The object never left the x-axis.
12. A very interesting result:
• Let us take all the distances travelled towards the right (that is., positive direction of the x-axis) as positive
• And all the distances travelled towards left (that is., negative direction of the x-axis) as negative
• Now we add the distances:
OA + AB + BC = 40 + 30 -50 = 20
• '20' is the magnitude of the final displacement
From the discussion so far in this chapter, we can write this:
■ To specify the position of an object, we need two items:
• Magnitude of the displacement
• Direction of the displacement
In the next section, we will see Uniform and Non-uniform motion.
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