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. $\frac{10}{3}m$
• B. $\frac{19}{3}m$
• C. $6\, m$
• D. $4\, m$

Answer 1

The Correct Option is A

To find the distance travelled by the particle in the third second, we can use the concept of motion under uniform acceleration. The particle starts from rest with an acceleration \( \frac{4}{3} \, \text{ms}^{-2} \).

The formula to calculate the distance travelled in the \( n \)-th second is given by:

S_n = u + \frac{1}{2} a (2n-1)

where \( u \) is the initial velocity, \( a \) is the acceleration, and \( n \) is the second for which we want to find the distance.

Since the particle starts from rest, \( u = 0 \). The acceleration \( a = \frac{4}{3} \, \text{ms}^{-2} \), and we need to find the distance for the third second (\( n = 3 \)).

Substitute the values into the formula:

S_3 = 0 + \frac{1}{2} \times \frac{4}{3} \times (2 \times 3 - 1)

Simplifying inside the parenthesis:

S_3 = \frac{1}{2} \times \frac{4}{3} \times 5 = \frac{1}{2} \times \frac{20}{3} = \frac{10}{3} \, m

Therefore, the distance travelled by the particle in the third second is \frac{10}{3} \, m, which matches the given correct answer.

Let's verify why the other options are incorrect:

• \frac{19}{3} \, m is incorrect because it results from an incorrect application of the formula or calculation error.
• 6 \, m is incorrect as it ignores the specific requirement of finding the distance for the third second.
• 4 \, m is incorrect, as it does not match the calculation demonstrated above.

The use of the distance travelled in the \( n \)-th second formula is crucial for solving this problem correctly. Understanding the differentiation between total distance and distance in a specific second is key. Remember, this approach can be used generally for similar problems, facilitating quicker solutions in exams.