Question

An object is moving along a straight line with initial velocity u and constant acceleration a. What is the

displacement of the particle in the nth second?​

Answer 1

Answer:

Displacement = ut + 1/2$an^2$

Explanation:

For this question we will use second equation of motion,

$S = ut + 1/2at^2$

where,

S is the displacement in metre.

u is the initial velocity in $m/s$.

t is is the time which substituted as n seconds.

a is the acceleration in $m/s^2$.

Answer 2

Given : An object is moving along a straight line with initial velocity u and constant acceleration a.

To Find :  displacement of the particle in the nth second?​

Solution :

Sₙ  - Sₙ₋₁

S = ut + (1/2)at²

= un + (1/2)a(n)²  -  (u(n-1) + (1/2)a(n-1)²)

= u +  (1/2)a ( n² - (n - 1)²)

= u + (1/2)a (2n - 1)(1)

= u + (a/2)(2n - 1)  

displacement of the particle in the nth second = u +  (a/2) (2n - 1)  

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