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NEET Physics QUESTION #1032
Question 1
In some units, time \(t\) and position \(x\) of a particle satisfy \(t = x^2 + x\). The acceleration of the particle is:
  • \(+\dfrac{2}{(x+1)^3}\)
  • \(+\dfrac{2}{2x+1}\)
  • \(-\dfrac{2}{(x+2)^3}\)
  • \(-\dfrac{2}{(2x+1)^3}\)✔️
Correct Answer Explanation
\(\frac{dt}{dx} = 2x+1\Rightarrow v = \frac{dx}{dt} = \frac{1}{2x+1}\). Acceleration: \(a = \frac{dv}{dt} = \frac{dv}{dx}\cdot v = \frac{-2}{(2x+1)^2}\cdot\frac{1}{2x+1} = \frac{-2}{(2x+1)^3}\).