A body initially at rest is moving with uniform acceleration a m/s².It’s velocity after n second is v.The displacement of the body in last 2s is

Options

(a) 2v(n-1)/n
(b) v(n-1)/n
(c) v(n+1)/n
(d) 2v(2n+1)/n

Correct Answer:

2v(n-1)/n

Explanation:

v = u + a t —-(1)
Let the velocity of the particle be v’ just two seconds before which means t=(n-2) seconds
Since initial velocity=0.
on applying eqn(1),
v’=0+a(n-2)
Now, S = u t + (1/2) a t²
So the displacement in the last two seconds is
Here the velocity before two seconds as found above is {(n-2)a}
which becomes initial velocity for last 2s and time is 2s because we want displacement for last 2s
S = {a (n-2) } 2 + (1/2) a (2²)
S = 2 a (n-2) + 2a
S= 2an-2a
S= 2a(n-1)
Acceleration is a=v/n
Displacement for last 2s = 2v(n-1)/n .