 |
| Position-Time Graph for Non-Uniform Motion |
|
| An object is said to be in non-uniform motion if it undergoes equal displacement in unequal intervals of time, however small these intervals may be |
| |
|
| a) If two objects A and B are moving with same velocity but have different initial positions, then their position-time graph will be |
| |
 |
| |
| b) If velocity VA > VB i.e., VA - VB is +ve |
| |
 |
| |
| [O represents position and time of meeting] |
| |
| c) If velocity VA < VB , VA - VB is -ve |
| |
 |
| |
| d) If the two objects are moving in a straight line in same direction with different velocities, then relative velocity of A w.r.t B is |
| |
| VAB = VA - VB |
| |
| e) If the two objects are moving in a straight line in opposite directions, then |
| |
| VAB = VA + VB |
| |
| The figure below shows the displacement-time graph of a moving particle. Consider any two points A and B on the graph. The coordinates of the points A and B are {x (t1), (t1)} and {x (t2), (t2)} respectively. |
| |
 |
| |
 |
| |
| Therefore, we conclude that the slope of the straight line joining two points on the displacement-time graph gives the average velocity of the particle between those two points. |
| |
|
| Suppose a particle is moving in such a way that its average velocity, measured for a number of different time intervals, is not constant. This particle is said to move with variable velocity. Then, we must determine a velocity of the particle at any given instant of time, called the instantaneous velocity. |
| |
| Instantaneous velocity of a particle is the limiting value of average velocity |
| |
 |
| |
 |
| |
The magnitude of the instantaneous velocity is known as
instantaneous speed. It is given by
 |
| |
| The speedometer of an automobile measures instantaneous speed. |
| |
|
| |
| Graphs are visual representations of the relationship existing between two variables, one of which is an independent variable and other is a dependent variable. One can calculate many physical quantities by calculating the slope of the graphs. Any inaccuracy in experimental data can be identified with the help of a graph. With graphs, one can find the mean value from a large number of observations. |
| |
| Let us discuss the graphical representation of an object in uniform motion. |
| |
