Question

.
A body starts from rest with uniform acceleration. The
velocity of the body after t seconds is v. The displacement
of the body in last three seconds is
3v (
3v​

Answer 1

Answer:

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