Question

The distance travelled by a particle starting from rest and moving with an acceleration \( \frac{4}{3} \) ms\(^{-2} \), in the third second is:

• A. \( 6 \) m
• B. \( 4 \) m
• C. \( \frac{10}{3} \) m
• D. \( \frac{19}{3} \) m

Hint:

The displacement in the \( n \)th second formula: \[ s_n = u + \frac{a}{2} (2n - 1) \] is useful for determining the exact distance covered in a given second without calculating total displacement.

Answer 1

The Correct Option is C

Step 1: {Use the nth second displacement formula} 
The displacement covered in the \( n \)th second is given by: \[ s_n = u + \frac{a}{2} (2n - 1) \] where: - \( u \) is the initial velocity, - \( a \) is the acceleration, - \( n \) is the time instant. 
Step 2: {Substituting values} 
Given: \[ u = 0, \quad a = \frac{4}{3} { ms}^{-2}, \quad n = 3 \] \[ s_3 = 0 + \frac{\frac{4}{3}}{2} (2(3) - 1) \] \[ = \frac{4}{6} \times 5 = \frac{10}{3} \,m \] Step 3: {Verify the options} 
Thus, the correct answer is (C) \( \frac{10}{3} \) m. 
 

Answer 2

Given:
- Initial velocity \( u = 0 \) (particle starts from rest)
- Constant acceleration \( a = \frac{4}{3} \, \text{m/s}^2 \)
- We need the **distance travelled in the 3rd second**

Step 1: Use formula for distance in the \( n \)th second
The formula for distance travelled in the \( n \)th second is:
\[ S_n = u + \frac{a}{2}(2n - 1) \]
Substitute the known values:
\[ S_3 = 0 + \frac{4}{3} \cdot \frac{1}{2}(2 \cdot 3 - 1) = \frac{4}{3} \cdot \frac{1}{2} \cdot 5 = \frac{4}{3} \cdot \frac{5}{2} = \frac{20}{6} = \frac{10}{3} \, \text{m} \]

Final Answer:
The distance travelled in the third second is \( \boxed{\frac{10}{3}} \, \text{m} \).