Question

The displacement of a body in 3rd second is 14m, in the fourth second it is 18m. Find the displacement of the body in the 9th second. PLEASE ANSWER FAST, I WILL MARK AS BRAINLIEST.

Answer 1

EXPLANATION.

we know that distance travelled by uniform

accelerated body is = nth seconds

$\bigstar\boxed{s_{n} \: = u \: + \frac{a}{2} (2n - 1)}$

To find displacement of a body in 9th seconds.

Sn = 14 m and n = 3

$14 = u \: + \: \frac{a}{2}(2(3) - 1)$

$14 = u \: + \frac{5a}{2} ....(1)$

Sn = 18 m and n = 4

$18 = u \: + \frac{a}{2} (2(4) - 1)$

$18 = u \: + \frac{7a}{2} ......(2)$

From equation (1) and (2) we get,

$- 4 = \frac{5a}{2} - \frac{7a}{2}$

$- 4 = \frac{ - 2a}{2}$

a = 4 m/s ^2

put the value of a = 4 m/s^2 in equation (1)

we get,

14 = u + 5 X 4 / 2

14 = u + 10

u = 4 m/s

Therefore,

according to the question,

n = 9

$s_{n} \: = 4 + \frac{4}{2} (2(9) - 1)$

$s_{n} \: = 4 + 34$

Sn = 38 m

Therefore,

displacement of a body in 9th seconds = 38 m