Question

A body moves from rest with a uniform acceleration of $4\text{ m/s}^2$. The distance covered by it in the 5th second of its motion is:

• A. 16 m
• B. 18 m
• C. 20 m
• D. 22 m Correct Answer: (B) 18 m

Hint:

For questions involving motion starting from rest ($u = 0$), the ratio of distances covered in successive seconds follows the sequence of odd numbers ($1 : 3 : 5 : 7 : 9 : \dots$). Since the distance in the 1st second is $\frac{a}{2} \times 1 = 2\text{ m}$, the distance in the 5th second will simply be the 5th odd number ($9$) multiplied by $2\text{ m}$, which immediately yields $18\text{ m}$!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
When an object undergoes uniformly accelerated rectilinear motion, we often need to distinguish between the total distance traveled during a given time interval and the specific distance covered during one particular second (such as the $n$-th second). The distance covered in the $n$-th second is the difference between the total displacement after $n$ seconds and the total displacement after $(n-1)$ seconds. This specific distance depends linearly on the acceleration and the numerical value of the specific second being analyzed.

Step 2: Key Formula or Approach:
The distance covered by a uniformly accelerating body during the $n$-th second is given by the kinematic formula: $$ S_n = u + \frac{a}{2}(2n - 1) $$ Where: - $S_n$ is the distance covered in the specific $n$-th second. - $u$ is the initial velocity of the body. - $a$ is the uniform acceleration. - $n$ is the specific second of the motion. From the given question parameters: - The body starts from rest, so initial velocity $u = 0\text{ m/s}$. - The uniform acceleration $a = 4\text{ m/s}^2$. - The specific second under consideration is $n = 5$.

Step 3: Detailed Explanation:
Let us substitute the given values directly into our kinematic formula: $$ S_5 = 0 + \frac{4}{2}\left(2(5) - 1\right) $$ Now, perform the arithmetic operations step-by-step: 1. Simplify the fraction outside the parenthesis: $$ \frac{4}{2} = 2 $$ 2. Evaluate the expression inside the parenthesis: $$ 2(5) - 1 = 10 - 1 = 9 $$ 3. Multiply the simplified components together: $$ S_5 = 2 \times 9 = 18\text{ m} $$ Therefore, the distance covered by the body in the 5th second is $18\text{ m}$, which corresponds perfectly to option (B).

Step 4: Final Answer:
The distance covered by the body in the 5th second of its motion is $18\text{ m}$.