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If the displacement, velocity and acceleration of a particle at time, $\mathrm{t}$ be $\mathrm{x}, \mathrm{v}$ and $\mathrm{f}$ respectively, then which one is true?
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Verified Answer
The correct answer is:
$f=-v^3 \frac{d^2 t}{d x^2}$
$$
\begin{aligned}
& \text { Hints: } \frac{d^2 t}{d x^2}=\frac{d\left(\frac{d t}{d x}\right)}{d x}=\frac{d\left(\frac{1}{v}\right)}{d x}=-\frac{1}{v^2} \frac{d v}{d t} \times \frac{1}{v} \\
& \Rightarrow f=-v^3 f \frac{d^2 t}{d x^2}
\end{aligned}
$$
\begin{aligned}
& \text { Hints: } \frac{d^2 t}{d x^2}=\frac{d\left(\frac{d t}{d x}\right)}{d x}=\frac{d\left(\frac{1}{v}\right)}{d x}=-\frac{1}{v^2} \frac{d v}{d t} \times \frac{1}{v} \\
& \Rightarrow f=-v^3 f \frac{d^2 t}{d x^2}
\end{aligned}
$$
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