If a body having initial velocity zero is moving with uniform acceleration $8 ext{ m/sec}^2$, then the dista

Question

If a body having initial velocity zero is moving with uniform acceleration $8 	ext{ m/sec}^2$, then the distance travelled by it in the fifth second will be:

TopperSquare Expert · Accepted Answer

The correct answer is Option (A): 36 metres. 1.  **Identify Given Values:**
    *   Initial velocity, $u = 0$.
    *   Uniform acceleration, $a = 8 	ext{ m/s}^2$.
    *   Time interval: The 5th second ($n = 5$).
2.  **Method 1: Using the n-th second formula**
    The distance travelled in the $n$-th second is given by $S_n = u + \frac{a}{2}(2n - 1)$.
    Substitute the values:
    $S_5 = 0 + \frac{8}{2}(2 	imes 5 - 1)$
    $S_5 = 4(10 - 1) = 4 	imes 9 = 36 	ext{ m}$.
3.  **Method 2: Difference in Displacement** 
    Calculate the position at $t=5$ and $t=4$ using $x = ut + \frac{1}{2}at^2$.
    *   $x_5 = 0(5) + \frac{1}{2}(8)(5)^2 = 4(25) = 100 	ext{ m}$.
    *   $x_4 = 0(4) + \frac{1}{2}(8)(4)^2 = 4(16) = 64 	ext{ m}$.
    *   Distance in 5th second $= x_5 - x_4 = 100 - 64 = 36 	ext{ m}$.
4.  **Method 3: Galileo's Law of Odd Numbers** 
    For a particle starting from rest with uniform acceleration, distances travelled in successive equal time intervals are in the ratio $1:3:5:7:9...$
    Distance in 1st second ($S_1$) = $\frac{1}{2}(8)(1)^2 = 4 	ext{ m}$.
    Distance in 5th second ($S_5$) corresponds to the 5th term (ratio 9).
    $S_5 = 9 	imes S_1 = 9 	imes 4 = 36 	ext{ m}$.

If a body having initial velocity zero is moving with uniform acceleration $8 \text{ m/sec}^2$ , then the distance travelled by it in the fifth second will be:

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If a body having initial velocity zero is moving with uniform acceleration 8 m/sec28 \text{ m/sec}^28 m/sec2, then the distance travelled by it in the fifth second will be: