Question

Derive the first equation of motion ( = + ) by graphical method​

Answer 1

Consider an object is moving with a uniform acceleration “a” along a straight line. The initial and final velocities of the object at time t = 0 and t = t are u and v respectively. During time t, let s be the total distance travelled by the object. In uniformly acceleration motion the velocity – time graph of an object is a straight line, inclined to the time axis.

OD = u; OC = v and OE = DA = t.

Let, the Initial velocity of the object = u

Let, the object is moving with uniform acceleration, a

Let, the object reaches at point B after time t, and its final velocity becomes, v.

Draw a line parallel to x-axis DA from point, D from where object starts moving.

Draw another line BA from point B parallel to Y-axis which meets at E at y-axis.

First Equation of Motion:

Let, OE = time (t)

From the graph:

BE = AB + AE

V = DC + OD (QAB = DC & AE = OD)

V = DC + v [QOD = u]

V = DC + V … (1)

Now, Acceleration (a) = Change in Velocity/ Time taken.

a = (v – u)/ t

a = (OC – OD)/ t = DC/ t

at = DC … (2)

By substituting the value of DC from (2) in (1):

We get:

V = at + u

V = u + at

It is the relation among initial velocity (u), final velocity (v), acceleration (a) and time (t).

It is called first equation of motion.