Q. The displacement of the body along $x -$ axis depends on time as $\sqrt{x} = t + 1$. Then the velocity of body
A) Increases with time
B) Decreases with time
C) Independent of time
D) None of these
Explanation
(a) $\sqrt{x} = t + 1$
Squaring both sides, we get
$x = (t + 1)^{2} = t^{2} + 2t + 1$
Differentiating it w.r.t time $t$, we get
$\frac{dx}{dt} = 2t + 2$
Velocity, $v = \frac{dx}{dt} = 2t + 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.