Derive equations of motion?

First equation of motion:

Consider a body having initial velocity u,If it is subjected to an acceleration 'a' so that after time 't' its velocity becomes v.

By the definition of acceleration

acceleration=Change in velocity/time taken

a=(v-u)/t

v=u+at

Second equation of motion:

Suppose the distance travelled by the above body in time t=s

we have average velocity=(Initial velocity+Final velocity)/2

Third equation of motion:

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Third Equation of Motion

Let 'u ' be the initial velocity of an object and a be the acceleration produced in the body. The distance travelled 'S ' in time 't ' is given by the area enclosed by the v - t graph.

graphical representation of III equation of motion

Graphical Derivation of Third Equation

S = area of the trapezium OABD.

Substituting the value of t in equation (1) we get,

III equation of motion

2aS = (v + u) (v - u)

(v + u)(v - u) = 2aS [using the identity a 2 - b 2 = (a+b) (a-b)]

v 2 - u 2 = 2aS III Equation of Motion

 

hope it helps u....

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