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

Position-time graph in relative velocity

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 V_A > V_B i.e., V_A - V_B is +ve

 

 

[O represents position and time of meeting]

c) If velocity V_A < V_B , V_A - V_B 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

V_AB = V_A - V_B

e) If the two objects are moving in a straight line in opposite directions, then

V_AB = V_A + V_B

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.

Instantaneous velocity

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 and its uses

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.