The distance travelled by a particle in a straight line motion is directly proportional to t1 / 2, where t is the time elapsed. What is the nature of motion?

Question

The distance travelled by a particle in a straight line motion is directly proportional to t1 / 2, where t is the time elapsed. What is the nature of motion? (A) Increasing acceleration (B) Decreasing acceleration (C) Increasing retardation (D) Decreasing retardation

Tardigrade Admin · Accepted Answer

s=k t1 / 2 ⇒ a=(d2 s/d t2)=-(1/4) k t-3 / 2 As t increases, retardation decreases.

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

Increasing acceleration

Decreasing acceleration

Increasing retardation

Decreasing retardation

$s = k t^{1/2}$
$\Rightarrow a = \frac{d ^{2} s}{d t ^{2}} = - \frac{1}{4} k t^{- 3/2}$
As $t$ increases, retardation decreases.

Q. The distance travelled by a particle in a straight line motion is directly proportional to t1/2, where t is the time elapsed. What is the nature of motion?