Question

a particle starts from rest with uniform acceleration a.its velocity after n seconds is v,then the displacement in the last two seconds will be

Answer 1

A particle starts from rest so,

initial velocity of particle ,

u = 0 

particle acceleration with uniform acceleration a 
So, particle must follow all kinematical equations .
 
I mean, S = ut + 1/2at² 

At u = 0,

S = 1/2at²

Here S is displacement during t time . 


∴ displacement in last 2 sec = distance travelled in n sec- distance travelled in (n -2) sec

= $\bold{S_n-S_{n-1}}$= 1/2 an² - 1/2a(n -2)² 
= 1/2 a (n² - n² + 4n - 4)
= a (2n -2) 
So, displacement in last 2 sec = a(2n - 2) 

A/C to question, 
Final velocity = v
Time = t 
Acceleration = a 
Then, use formula, 
v = u + at 
initial rest so, u = 0 
v = a × n ⇒a = v/n 
Now, displacement in last 2 sec = v/n(2n - 2) = 2v - 2v/n 

Answer 2

hope you could understand my solution