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
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:
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 Derivation of Third Equation
S = area of the trapezium OABD.
Substituting the value of t in equation (1) we get,
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....