CBSE Class 11-science Answered

Let u be initial velocity and v be final velocity at end of the time t .

Acceleration a is defines as rate of change of velocity with respect to time.

Acceleration a = ( v - u ) / t  .......... ...........(1)

Hence we get , v = u + a t ..........................(2)

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Let u be initial velocity and v be final velocity at end of the travel distance S

Distance travelled S = ( average velocity ) × time

average velocity = ( v + u ) / 2

Hence , Distance travelled  S = [ ( v + u ) / 2 ] × t  .....................................(3)

By substituting time t from eqn.(1) , we rewrite above equation (3) as

S = [ ( v + u ) / 2 ] × [ ( v - u ) / a ]

S = ( v² - u² ) / ( 2 a )

2 a S = ( v² - u² )

v² = u² + ( 2 a S )