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 accelerationB- Decreasing accelerationC- Increasing retardationD- Decreasing retardation

The correct option is D Decreasing retardationS∝ t^12 ⇒ S=kt^12 (where k is a constant) To get acceleration we need to differentiate s twice ⇒ a=d^2Sdt^2= 14kt ...

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Standard XII

Physics

Differentiation

The displacem...

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?

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
$S \propto t^{\frac{1}{2}}$
$\Rightarrow S = k t^{\frac{1}{2}}$ (where $k$ is a constant)
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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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 (where k is a constant) 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?