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: {Apply the formula for displacement in the nth second}
The displacement during the \( n \)th second is calculated using the formula: \[ s_n = u + \frac{a}{2} (2n - 1) \] with \( u \) representing initial velocity, \( a \) representing acceleration, and \( n \) representing the specific time instant. 
Step 2: {Input given parameters} 
The provided values are: \[ u = 0, \quad a = \frac{4}{3} { ms}^{-2}, \quad n = 3 \] Substituting these into the formula: \[ s_3 = 0 + \frac{\frac{4}{3}}{2} (2(3) - 1) \] \[ = \frac{4}{6} \times 5 = \frac{10}{3} \,m \] Step 3: {Confirm the result against options} 
The calculated displacement matches option (C) \( \frac{10}{3} \) m.