Question

In the third second, the distance traveled by a particle starting from rest and traveling with an acceleration of $4/3{\mathrm{ms}}^{-2}$ is

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

Answer 1

The correct option is A

$\left(\frac{10}{3}\right)m$

Step: 1 Given data:

Acceleration is $\alpha$$=$ $4/3{\mathrm{ms}}^{-2}$.

Time is $n=3$

Initial speed is $u=0$

Step: 2 Formula used:

The distance traveled in $n^{th}$ second can be computed using the following formula:

$S_n=u+\frac{1}{2}a\left(2n-1\right)\dots \dots \dots \dots \dots \dots \left(1\right)$

Step: 3 Calculate acceleration:

Substitute the known values in equation $\left(1\right)$,

$\begin{array}{rcl}{S}_{3^{rd}}& =& 0+\frac{1}{2}\times \frac{4}{3}\left(2\times 3-1\right)\\ & =& \frac{2}{3}\times 5\\ & =& \frac{10}{3}m\end{array}$

Hence option A is correct.