In our dialy life ,we see lots of things moving around for example car passing through from one place to other ,person riding on a bicycle and many more like this.
In scientific terms an object is said to be in motion ,if it changes its position with the pasage of time and if it does not change it position with the passage of time then it is said to be at rest
Both the motion and rest are relative terms for example mobile kept on the table is resting at its position but it is moving in the sense as earth is rotating on its axis.So for a person seeing mobile from earth it is at rest and for person on moon earth seems to change its position with time and so mobile is moving.
Simplest case of motion is rectilinear motion which is the motion of the object in a straight line
In our descriotion of object ,we will treat the object as an point object
Object under consideration can be treated as point object if the size of the object is much smaller than the distance travelled by it in a reasonable time duration for example length of a motor car travelling a distance of 500km can be neglected w.r.t distance travelled by it.
Here in kinematics ,we study ways to describe the motion without going into the cause of the motion
2.Position and Displacement
(a) Position:
To locate the position in motion or at rest,we need a frame of refrence.
Simplest way to choose a frame of refrence is to choose three mutually perpendicular axis labelled as X-,Y- and Z- axis as shown in figure below
Such system of labelling position of an object is known as rectangular coordinates system
If A(x,y,z) be the position of any point in rectangular co-ordinates system it can be labelled as follows
Point O is the point of intersection of these mutaully perpendicular axis and is known as refrence point or origin of frame of refrence
To measure a time ,we can also attach a clock with this frame of refrence
If any or all co-ordinates of the object under consideration changes with time in this frame of refrence then the object is said to be in a motion w.r.t the frame of the refrence otherwise it is at rest
For describing motion in one dimension we need one set of co-ordinates axis i.e only one of X,Y and Z axis
Similary for two and three dimensions we need two or three set of axis respectively
Motion of an object along a straight line is an example of motion in one dimension
For such a motion,any one axis say X-axis may be choosen so as to co-incide with the path along which object is moving
Position of the object can be measured w.r.t origin O shown in the figure
Position to the right of the origin has positive values and those to the left of origin O has negative values.
(b) Distance and displacement:
In the graph shown below an object is at position P at time t1 and at position R at time t2.
In the time interval from t1 to t2 particle has travelled path PQR and length of the path PQR is the distance travelled by the object in the time interval t1 to t2
Now connect the initial position of the object P with its final position R through a straight line and we get the displacement of the object.
Displacement of the object has both magnitude and direction i.e., displacement is a vector quantity.
Magnitude of displacement vector is equal to the length of straight line joining initial and final position and its direction points from the initial position of object towards its final position.
In contrast to displacement distance is scalar quantity.
Question:
A particle is thrown vertically upwards. It reaches the height H and the come downward.What is the distance and displacement in the whole motion?
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