The distance travelled by a body in the nth second is given by the expression $(2 + 3 n)$ . Find the initial velocity and acceleration. Also, find its velocity at the end of $2$ seconds.

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Solution

Consider the distance traveled by an object in nth second $= n + \frac{1}{2} a (2 n - 1)$

So,

$\begin{matrix} 2 + 3 n = u + \frac{1}{2} a (2 n - 1) \Rightarrow 2 + 3 n = u + a n - \frac{a}{2} \end{matrix}$

Now equating both parts

$\begin{matrix} a n = 3 n \Rightarrow a = 3 m / s^{2} 2 = u - \frac{a}{2} \Rightarrow u = \frac{7}{2} = 3.5 m / s \end{matrix}$

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