an object of mass m is moving along x axis such that its position x is proportional to t^1/2 where t is time then magnitude of acceleration is
Answers
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Answer:
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} } }x∝
t
2
1
\displaystyle \sf{ \implies \: x = \frac{k}{ {t}^{2} } }⟹x=
t
2
k
Differentiating both sides with respect to t we get
\displaystyle \sf{ v = \frac{dx}{dt} = \frac{ - 2k}{ {t}^{3} } }v=
dt
dx
=
t
3
−2k
Again Differentiating both sides with respect to t we get
\displaystyle \sf{ f = \frac{dv}{dt} = \frac{ 6k}{ {t}^{4} } }f=
dt
dv
=
t
4
6k
\displaystyle \sf{ \therefore \: \: f \propto \frac{1}{ {t}^{4} } }∴f∝
t
4
1
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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