Question

A particle starts from rest with uniform acceleration a. Its velocity after n seconds is v. The displacement of the particle in the last two seconds is?

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
= Sn - Sn-2 = 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)

according 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