Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
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?
MathematicsApplication of DerivativesWBJEEWBJEE 2010
Options:
  • A $\mathrm{f}=\mathrm{v}^3 \frac{\mathrm{d}^2 t}{d \mathrm{x}^2}$
  • B $f=-v^3 \frac{d^2 t}{d x^2}$
  • C $\mathrm{f}=\mathrm{v}^2 \frac{\mathrm{d}^2 \mathrm{t}}{\mathrm{dx}^2}$
  • D $f=-v^2 \frac{d^2 t}{d x^2}$
Solution:
1729 Upvotes Verified Answer
The correct answer is: $f=-v^3 \frac{d^2 t}{d x^2}$
$$
\begin{aligned}
& \text { Hints: } \frac{d^2 t}{d x^2}=\frac{d\left(\frac{d t}{d x}\right)}{d x}=\frac{d\left(\frac{1}{v}\right)}{d x}=-\frac{1}{v^2} \frac{d v}{d t} \times \frac{1}{v} \\
& \Rightarrow f=-v^3 f \frac{d^2 t}{d x^2}
\end{aligned}
$$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.