Question

Two uses of graphical representation of
Motion

Answer 1

A graph is a pictorial representation of the relation between two sets of data of which one set is of dependent variables and the other set is of independent variables.

In a displacement-time graph, displacement is a dependent quantity, taken on the Y-axis and time is taken on the X-axis, as it is independent. If the position of an object changes with respect to the reference position and time, it is said to be in motion.

The velocity at any instant of time is called instantaneous velocity. A positive slope of velocity-time graph gives acceleration and a negative slope gives deceleration or retardation of the object.

For an object moving with uniform acceleration, we have the following equations of motion,

v = u + at

s= ut +½ at2

v2 - u2 = 2as

Sn= u+a(n - ½)

Where u = Initial velocity,
s = Displacement,
a = Acceleration,
t = Time and
v = Final velocity
Sn = The displacement of the body in n th second
n = n th second

If an object moves along a straight path, it is in a linear motion. If an object covers equal angular displacements in equal intervals of time then it is said to be in uniform circular motion. If an object repeats its motion on the path in regular intervals of time than it is in periodic motion.

Displacement-Time Graph
In the displacement-time graph, the time is taken on X-axis and the displacement of body is taken on Y-axis. From this graph, we can determine the velocity of body. Since, velocity is the ratio of displacement and time therefore the slope of displacement-time graph gives the velocity. If the is positve, it implies that the body is moving away from the starting point.

If a body moves in a straight path the distance and the displacement of the motions are equal so the Displacement - Time graph and the Distance - Time graph are same.

(i) If the graph is parallel to time axis, then body is stationary.