InterviewSolution
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InterviewSolution
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Suppose displacement `y(t)` (that is, y as a function of t ) is given by `y(t)=t^(3)` |
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Answer» Find velocity `(dy//dt)` at `t = 3 sec`. Displacement at `t+Deltat` is `y(t+Deltat)=(t+Deltat)^(3)` `=(t^(3)+3t^(2)Deltat+3t Deltat^(2)+Deltat^(3))` hence displacement from t to `t+Deltat` is `Deltay` `Deltay=y(t+Deltat)-y(t)=(3t^(2)Deltat+3tDeltat^(2)+Deltat^(3))` Substituting this into Equation (i) gives `(dy)/(dt)=underset(Deltararr0)(lim)(Deltay)/(Deltat)=underset(Deltatrarr0)(lim)[3t^(2)+3tDeltat+Deltat^(2)]` Here we can see that if we take very small value of `Deltat` then value of `dy//dt` will approach `3t^(2)` as all other terms will become negligible and impossible to measure by any instrument available in this world. hence, `" " (dy)/(dt)=3t^(2) rArr (dy)/(dt)=v(at " " t =3sec)=3(3)^(2)=27 m//s` |
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