CBSE Class 9 Answered

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

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 ABt₁t₂
S = Area of triangle ABA’ + Area of rectangle AA’t₂t₁  = Area of trapezium
S = ½  x Sum of parallel sides x Perpendicular distance
 ....... (Equation 1)
From the first equation of motion, v = u + at; 

Substituting in equation 1, we get 

or,  v² – u² = 2as
which is the required equation of motion.