Question

The displacement of a body along $x-$ axis depends on time as $\sqrt{x}=3t+5$ Then the velocity of body

• A. Increase with time
• B. Independent of time
• C. Decrease with time
• D. None of these

Answer 1

Answer: (A)

$\sqrt{x}=3t+5$
Squaring both side
$\begin{array}{rl}<br/>(\sqrt{x}{)}^2& =(3t+5{)}^2\\ <br/>x& =9t^2+25+30t<br/>\end{array}$
Differentiate both side
$\frac{dx}{dt}=\frac{d\left(9t^2+30t+25\right)}{dt}$
$V=18t+30$
Velocity will increase with time.