Motion in a Straight Line
When an object moves along one straight line or in one dimension such a type of motion is motion in a straight line. The motion of the object may take place in one dimension along a straight line or in two dimension in a plane or in three dimensions in space. However, the object along a straight line is the simplest of all the types of motions. Such a motion can be described by plotting the graph between the time and the position of the object.
Consider the motion of a man traveling by his car from his home to some distant destination. To describe the motion graphically we must know the position of the man at different instances of time. For this, we must choose some suitable unit of length for position measurement (which in this case may be a kilometer) and some suitable unit for measuring time (within this case maybe an hour). In addition to the units of length and time, the following have to be chosen:
- Origin for position and direction for position measurement.
- Origin for time and sense of the passage of time.
In order to explain, consider that the man lives his home point O at 8 a.m. by car crosses a city A at 11:00 a.m. reaches another city B at 12 noon and finally reaches his destination P at 2:00 p.m. If the distance of city A, city B, and his destination P from his home are 60 km, 80 km, and 130 km respectively then this information about the motion of the man can be summarised as given in figure.
Let us now understand the meaning of origin for position direction for position measurement, reason for time and sense of passage of time separately.
1. Origin for position and direction for position measurement
Let us consider home for of the man as the origin for position. If motion is represented along the straight line OX that is x-axis, then x = 0, x = 60 km, x = 80 km and x = 130 km when the man leaves his home O (origin for position) crosses the city A, crosses the city B and reaches his destination P respectively. Therefore, home of the man is chosen as origin for position the information regarding the position of the man during the course of journey may be summarised as in figure.
Now consider that the city a is to be chosen as the origin for position. Obviously when the man is at A, x = 0. Further, x = 20 km and x = 70 KM when the man crosses the city B and reaches the destination P. On the other hand x = – 60, left his home to start the journey. Therefore when the city A is chosen as the origin of for position the information regarding the position of the man during the course of journey maybe summarize as shown in the figure.
From the above discussion, following points maybe noted:
- The distance measured to the right of the origin of the position axis is taken as positive and the distance measured to the left of the origin is taken as negative.
It may be pointed out that in case the motion is along vertical line; the distance covered above the origin of position axis will be taken as positive and that below the origin as negative - The origin for position can be shifted to any point on the position axis.
- The distance between two points on position access is not affected due to the shift in the origin of position axis.
2. Origin for time and sense of passage of time
Again, latest cons instant when the man left his home that is 8:00 a.m. as the origin for time. Therefore when the man lives his home, crosses city A then city B and finally reaches his destination P, t = 0, t = 3h, t = 4h and t = 6h respectively. Therefore, when 8 a.m. is chosen as origin for time the information regarding time when the man is at different positions may be summarise as shown in the given figure.
Now, that the instant 12 noon is chosen as origin for time. Obviously, t =2h, h when a man reaches the destination P and t = -1h, when the man cross the city B and t = -4h, when he left his home. Therefore, when 12 noon is chosen as the origin for time; the information regarding time, when the man is at different position maybe summarise as soon in picture.
From the above discussion, the following points may be noted:
- The time measured to the right of the origin of the time axis is taken as positive and the time measured to the left of the origin is taken as negative.
- The origin of the time axis can be shifted to any point on the time axis.
- The negative time coordinate of a point on time Axis means that object reach that point a time that much before the origin of the time axis i.e. t = 0.
- The time interval between two points on time axis is not affected due to the shift in the origin of time axis.
The figure 2 and 3 provide information regarding the motion of the man as far as his position is concerned, while the figure 5 and 6 provide information regarding the instance of time when the man is a different positions. Latest now summarise the information regarding both position and time about the motion of the man in the same figure in the following two cases:
1. When the same point is chosen as origins for position and time
Suppose that when the man leaves his home O at 8:00 a.m., the point O is chosen as origin for position and the instant 8:00 a.m. is chosen as origin for time. Then, information regarding the motion of the man both about his position and time may be recorded in the same figure.
2. When the different points are chosen as origins for position and time
Suppose that the point B is chosen as the origin for position and the instant, man was at a that is 11 a.m. as the origin for time. The information regarding the motion of the man about this position and time maybe recorded as shown in figure.
