Question

A body starts from rest and moves with uniform acceleration. The ratio of distance covered in 4th and 3rd seconds is:

• A. 4:3
• B. 7:5
• C. 16:9
• D. 5:7

Hint:

For $u=0$, distances in successive seconds follow the ratio of odd numbers: 1 : 3 : 5 : 7...

Answer 1

The Correct Option is B

Step 1: Concept
The distance covered in the $n^{th}$ second of motion is given by the formula: $S_{n} = u + \frac{a}{2}(2n - 1)$.

Step 2: Meaning
Since the body starts from rest, the initial velocity $u = 0$. The formula simplifies to $S_{n} \propto (2n - 1)$.

Step 3: Analysis
For the 4th second ($n=4$): $S_{4} = \frac{a}{2}(2 \times 4 - 1) = \frac{7a}{2}$. For the 3rd second ($n=3$): $S_{3} = \frac{a}{2}(2 \times 3 - 1) = \frac{5a}{2}$.

Step 4: Conclusion
The ratio $S_{4} : S_{3}$ is $\frac{7a/2}{5a/2} = 7:5$. Final Answer: (B)