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Answer:
Three Equations of Motion are v = u + at; s = ut + (1/2) at² and v² = u² + 2as and these can be derived with the help of velocity time graphs using definition acceleration.
Ans. 48
Equations of motion by graphical method. Consider an object moving along a straight line with initial velocity u and uniform acceleration a. ... 8.19, its velocity-time graph is straight line. Here OA = ED = u, OC = EB = v and OE = t = AD.
Ans. 49
Given that a body is travelling at uniform acceleration along a straight line with initial velocity u and final velocity v at time t.
Acceleration a = v-u / t
at = v - u
v = u + at ---------------------------- (1)
Distance s = velocity * time
s = (u+v)/2 * t
s = (u + u + at) /2 * t
s = (2u/2 + at/2)t
s = ut +1/2*at^2 -------------------- (2)
Squaring both sides of equation 1, we get:
v^2 = (u+at)^2
= u^2 + a^2t^2 + 2uat
= u^2 + 2a (ut +1/2 at^2)
v^2 = u^2 + 2as ---------------------- (3)
Thus we have 3 equations of motion.