Question

question no.37 please answer

Answer 1

HELLO THERE!

We can use Integration to find out the expression for distance travelled in nth seconds.

By definition of velocity,

$v=\frac{dS}{dt}$

(where v is the final velocity, t is the time taken, and S is the displacement).

or dS = v.dt

=> dS = (u + at) dt .... (i) [∵v = u + at]

When time = (n-1) seconds, let displacement travelled = S₁ metres.

When time = n seconds, displacement travelled = S₂ metres.

Integrating equation (i) within the above limits of time and distance, we get the relation mentioned in the attachment.

On further solving, we get the expression:

$S_{n} = u+\frac{a}{2}(2n-1)$

Where,

$S_{nth} = S_{n} - S_{n-1}$

(Displacement in nth second).