Question

The displacement travelled by a particle in a straight-line motion is directly proportional to $t^{1/2}$, where $t=$ time elapsed. What is the nature of motion?

• A. Increasing acceleration
• B. Decreasing acceleration
• C. Increasing retardation
• D. Decreasing retardation

Answer 1

The correct option is D Decreasing retardation

$S\propto t^{\frac{1}{2}}$
$\Rightarrow S=k{t}^{\frac{1}{2}}$
To get acceleration we need to differentiate $s$ twice
$\Rightarrow a=\frac{d^{2}S}{d{t}^2}=-\frac{1}{4}k{t}^{-3/2}$
Negative sign indicates that it is retardation and as its value is decreasing with time so, it is decreasing retardation.