Question

body starts from rest and moves with an acceleration of 10 metre per second square find the displacement in fourth of its motion​

Answer 1

Correct question:-

A body starts from rest and moves with an acceleration of 10 m/s². Find the displacement in fourth second of its motion.

Given:-

• Initial velocity = u = 0 m/s
• Acceleration = a = 10 m/s²
• $\sf n^{th}$ second = $\sf 4^{th}$

To find:-

• Displacement in $\sf 4^{th}$ second = $\sf S_{4^{th} }$ = ?

Answer:-

❖ Note that displacement in n seconds and the displacement in $\sf n^{th}$ second is different. Displacement in $\sf n^{th}$ is (Displacement in n seconds) - (Displacement in (n - 1) seconds).

❖ Also, it is WRONG to write that displacement in $\sf n^{th}$ is (Displacement in (n + 1) seconds) - (Displacement in n seconds).

Formula:

❖ $\sf S_{n^{th} } = u + \dfrac{1}{2}a(2n - 1)$

So, on putting the values given in the question, we get,

$\sf \longrightarrow S_{4^{th} } = 0 + \dfrac{1}{2}10\{(2\times 4) - 1 \}$

$\sf \longrightarrow S_{4^{th} } = 5(8 - 1)$

$\sf \longrightarrow S_{4^{th} } = 5 \times 7$

$\longrightarrow \underline{\underline{\sf{\green{ S_{4^{th} } = 35 \: metres }}}}$