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?

Increasing acceleration

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Decreasing acceleration

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Increasing retardation

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Decreasing retardation

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Solution

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.

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Similar questions

Figure shows the velocity-time graph of a particle moving in a straight line.

(i) State the nature of motion of particle.

(ii) Find the displacement of particle at t=6 s.

(iii) Does the particle change its direction of motion?

(iv) Compare the distance travelled by the particle from 0 to 4 s and from 4 s to 6 s.

(v) Find the acceleration from 0 to 4 s and retardation from 4 s to 6 s.

Q. 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?

Q. The distance travelled by a particle is directly proportional to

t^{1 / 2}

, where 't' is time elapsed. What is the nature of motion?

Q. The velocity of a particle moving in a straight line is directly proportional to

{\frac{3}{4}}^{t h}

power of time elapsed. The ratio of its displacement and acceleration be

t^{x}

.Find

x .

If in case of a motion, displacement is directly proportional to the square of time elapsed, what do you think about its (A) velocity (B) acceleration?

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

The correct option is D Decreasing retardationS∝t12 ⇒S=kt12 To get acceleration we need to differentiate s twice ⇒a=d2Sdt2=−14kt−3/2 Negative sign indicates that it is retardation and as its value is decreasing with time so, it is decreasing retardation.

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?