Question

An object of mass m is moving along x-axis such that its position x is proportional to 1/t² where t is time, then magnitude of its acceleration is



Increasing with time

Is constant

Is decreasing with time

None of these
​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

An object of mass m is moving along x-axis such that its position x is proportional to 1/t² where t is time, then magnitude of its acceleration is

• Increasing with time

• Is constant

• Is decreasing with time

• None of these

EVALUATION

Here it is given that

$\displaystyle \sf{x \propto \frac{1}{ {t}^{2} } }$

$\displaystyle \sf{ \implies \: x = \frac{k}{ {t}^{2} } }$

Differentiating both sides with respect to t we get

$\displaystyle \sf{ v = \frac{dx}{dt} = \frac{ - 2k}{ {t}^{3} } }$

Again Differentiating both sides with respect to t we get

$\displaystyle \sf{ f = \frac{dv}{dt} = \frac{ 6k}{ {t}^{4} } }$

$\displaystyle \sf{ \therefore \: \: f \propto \frac{1}{ {t}^{4} } }$

Thus as time increases magnitude of its acceleration will decrease

FINAL ANSWER

Hence the correct option is

Is decreasing with time

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