miller indices

1. In this, we will plot few graphs between distance and time, velocity and time and
acceleration and time. Some names are also given to these graphs like :
i) Position time graph (x – t graph)
ii) Velocity time graph
iii) Acceleration time graph

2. The motion of an object moving in a straight line is studied by the position time
graph. For this a graph is plotted by taking the time on x axis and position on y
axis. It is called the position time (or x-t graph). The points on the graph
corresponding to positions at different instants are joined by a smooth curve (or a
straight line). Generally the origin of position and origin of time coincide.

4. If the position of an object does not change with time, the object is said to be in
the state of rest. In such a case, the position of object remains the same at each
instant, i.e., x=x (constant) for such an object, the position – time graph will be a
straight line parallel to the time axis. For example, a train standing on a platform,
a bus standing on its stoppage etc.

5. If the position of a body changes by an equal amount in equal intervals of time (i.e., velocity of
body is said to be the uniform motion. For such a motion, the position – time graph is straight
line inclined to the time axis. If the straight line makes an acute angle with the time axis, then
the displacement increases with time (i.e., the body is moving away from its initial position)
and if the straight line makes an obtuse angle with the time axis, then the displacement
decreases with the increase in time (i.e., the body is coming back towards its initial position).

7. If the velocity of body is variable i.e. there is either
acceleration or retardation in motion of body, the
position – time graph will be a curve. Figure shows
the position – time graph for a uniformly accelerated
motion.

9. If a graph is plotted by taking the velocity of a
moving object along y – axis and time on x –
axis, it is called the velocity time graph of that
object.

10. In a uniform motion, since velocity of object does not
change with time, so the velocity – time graph is a straight
line parallel to the time axis. Figure represents the
velocity time graph for a body moving with a constant
velocity.

12. In a uniformly accelerated motion, the increase in velocity is some
interval of time (i.e., in one dimensional motion, the magnitude of
velocity increases at a uniform rate).
For such a motion, the velocity – time graph plotted by taking the
velocity on y - axis and time on x – axis will be a straight line inclined
at an acute angle with the time axis.

14. If acceleration of motion in non – uniform i.e.,
there is unequal change in velocity in same
interval of time, the v – t graph will be a curve.

15. If a graph is plotted by taking acceleration on y –
axis and time on x – axis, the graph is called the
acceleration – time graph.

16. If an object is at rest or it is moving with the uniform
velocity, its acceleration will be zero. In such a case,
the acceleration – time graph will be a straight line
coinciding with the time axis as shown in figure.

18. If the velocity of an object increases at a uniform rate, its acceleration
will be uniform (or constant) and positive. For example, if an object is
freely released to fall downwards, its velocity will increase by 9.8 m/s in
each second. In such a case, the acceleration – time graph will be a
straight line parallel to the time axis as shown in figure.

20. If the velocity of a body decreases at a uniform rate, the acceleration
will be constant and negative. For example, if an object is thrown
vertically upwards, its velocity will decrease by 9.8 m/s in each second.
In such a case, the acceleration – time graph will be a straight line
parallel to the time axis as shown in figure.