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Grade 11Mechanics

a particle starts from rest with uniform acceleration a. it's velocity after ‘n’ second is ‘v’. The the displacement of the body in the last 2 seconds is
  1. 2v(n-1)/n
  2. v(n-1)/n
  3. v(n+1)/n
  4. 2v(2n+1)/n

Profile image of Dishari Das
7 Years agoGrade 11
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1 Answer

Profile image of Arun
ApprovedApproved Tutor Answer7 Years ago
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
=  = 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