Question

A body starts moving with an initial velocity of $um{s}^{-1}$ and an acceleration of $4m{s}^{-2}$. If the distance traveled by it is $20m$ in the $2seconds$, then the value of $u$ is ___________.

• A. $41m{s}^{–1}$
• B. $14m{s}^{–1}$
• C. $5m{s}^{–1}$
• D. $10m{s}^{–1}$

Answer 1

The correct option is B

$14m{s}^{–1}$

Step 1: Given:

$u$is the initial velocity of the body.
$$\begin{gathered} \mathrm{a}=4{\mathrm{ms}}^{–2};\mathrm{n}=2^{\mathrm{nd}}\mathrm{s}{\mathrm{S}}_2=20\mathrm{m} \\ \mathrm{u}=? \end{gathered}$$

Step 2: Formula used

The distance traveled by a body in the nth second is given by $S_n=u+\frac{a}{2}(2n-1)$

Step 3: Calculation for initial velocity

On putting the given value in the above formula

$$\begin{gathered} S_2=u+a(n-\frac{1}{2})=u+a(2-\frac{1}{2})=u+\frac{3}{2}a \\ u=S_2-4\left(\frac{3}{2}\right)=20-6=14m{s}^{-1} \end{gathered}$$

Hence, the correct option is (B).