Question

A body with an initial velocity of $18\frac{km}{h}$ accelerates uniformly at the rate of $3\frac{cm}{s^2}$ over a distance of 200 m in $t$ s. What will be its be its velocity at time $t$?

• A. $27\frac{m}{s}$
• B. $37\frac{m}{s}$
• C. $\sqrt{27}\frac{m}{s}$
• D. $\sqrt{37}\frac{m}{s}$

Answer 1

The correct option is D

$\sqrt{37}\frac{m}{s}$

Let, the final velocity be $v$

Given, acceleration $a=3\frac{cm}{s^2}$

$=\frac{3}{100}\frac{m}{s^2}$

$=0.03\frac{m}{s^2}$

Initial velocity $u=18\frac{km}{h}$

$=18\times \frac{1000m}{3600s}$

$=5\frac{m}{s}$

Distance $S=200m$

We know,

$v^2-u^2=2aS$

So, final velocity $v=\sqrt{2aS+u^2}$

$\Rightarrow v=\sqrt{[2\times 0.03\times 200]+5^2}$

$\Rightarrow v=\sqrt{12+25}$

$\Rightarrow v=\sqrt{37}\frac{m}{s}$