Question

If a car starting from rest moving with
uniform acceleration suffers (5/9)th of its
total displacement in nth second of its
journey then n is
(A) 5
(B) 3
& Ę
(C) 9
(D) 2​

Answer 1

The value of n is 3

Therefore, option (B) is correct.

Step-by-step explanation:

If the acceleration of the car is a

Then total displacement in n second

$s=0\times n+\frac{1}{2}an^2$

$\implies s=\frac{1}{2}an^2$   ......... (1)

Displacement in nth second = Displacement in n seconds - Displacement in (n-1) seconds

$\implies s'=\frac{1}{2}an^2-\frac{1}{2}a(n-1)^2$

But s' = (5/9)s

Therefore,

$\frac{5}{9}s=s-\frac{1}{2}a(n-1)^2$

$\implies \frac{4}{9}s=\frac{1}{2}a(n-1)^2$   ..... (2)

Dividing eq (2) by (1)

$\frac{4}{9}=\frac{(n-1)^2}{n^2}$

$\implies (\frac{n-1}{n})^2=(\frac{2}{3})^2$

$\implies \frac{n-1}{n}=\pm\frac{2}{3}$

$\implies 1-\frac{1}{n}=\pm\frac{2}{3}$

Taking positive sign

$1-\frac{1}{n}=\frac{2}{3}$

$\implies \frac{1}{n}=1-\frac{2}{3}$

$\implies \frac{1}{n}=\frac{1}{3}$

$\implies n=3$

Taking negative sign

$1-\frac{1}{n}=-\frac{2}{3}$

$\implies \frac{1}{n}=1+\frac{2}{3}$

$\implies \frac{1}{n}=\frac{5}{3}$

$\implies n=3/5$

But n must be a whole number

Therefore,

n = 3

Hope this answer is helpful.

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