Question

derive graphically the third equation of motion , v2=u2-2as​

Answer 1

Explanation:

Consider the velocity-time graph for a body having some non zero initial velocity at time t = 0.

image

u: velocity at time t1

v: velocity at time t2

a: uniform acceleration of the body along the straight line

Displacement covered during the time interval t2 - t1 = Area ABt1 t2

S = Area of triangle ABA’ + Area of rectangle AA’t2 t1 = Area of trapezium

S = ½ x Sum of parallel sides x Perpendicular distance

image

… (Equation 1)

From the first equation of motion, v = u + at;

image

Substituting in equation 1, we get

image

or, v2 – u2 = 2as

which is the required equation of motion.