FRAME OF REFERENCE:
we need to use a reference point and a set of axes. It is convenient to choose a rectangular coordinate system consisting of three mutually perpendicular axes, labeled X-, Y-, and Z- axes.
The point of intersection of these three axes is called origin (O) and serves as the reference point. The coordinates (x, y. z) of an object describe the position of the object with respect to this coordinate system.
To measure time, we position a clock in this system. This coordinate system along with a clock constitutes a frame of reference.
Description of an event depends on the frame of reference chosen for the description. For example, when you say that a car is moving on a road, you are describing the car with respect to a frame of reference attached to you or to the ground. But with respect to a frame of reference attached with a person sitting in the car, the car is at rest.
To describe motion along a straight line, we can choose an axis, say X-axis, so that it coincides with the path of the object.
Displacement has both magnitude and direction. Such quantities are represented by vectors.
If one or more coordinates of an object change with time, we say that the object is in motion. Otherwise, the object is said to be at rest with respect to this frame of reference.
The choice of a set of axes in a frame of reference depends upon the situation. For example, for describing motion in one dimension, we need only one axis. To describe motion in two/three dimensions, we need a set of two/ three axes.
The magnitude of displacement may or may not be equal to the path length traversed by an object.
The magnitude of the displacement for a course of motion may be zero but the corresponding path length is not zero. For example, if the car starts from O, goes to P and then returns to O, the final position coincides with the initial position and the displacement is zero. However, the path length of this journey is OP + PO.
Motion of an object can be represented by a position-time graph as you have already learnt about it. Such a graph is a powerful tool to represent and analyse different aspects of motion of an object. For motion along a straight line, say X-axis, only x-coordinate varies with time and we have an x-t graph. Let us first consider the simple case in which an object is stationary, e.g. a car standing still at x = 40 m. The position-time graph is a straight line parallel to the time axis, as shown in Fig.
If an object moving along the straight line covers equal distances in equal intervals of time, it is said to be in uniform motion along a straight line.The following figure shows the position-time graph of such a motion.
Now, let us consider the motion of a car that starts from rest at time t = 0 s from the origin O and picks up speed till t = 10 s and thereafter moves with uniform speed till t = 18 s. Then the brakes are applied and the car stops at t = 20 s and x = 296 m. The position-time graph for this case is shown in Figure below.
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