In some appropriate units, the time (t) and position (x) relation of a moving particle is given by t=x^2+x. The acceleration of t…

Question

In some appropriate units, the time (t) and position (x) relation of a moving particle is given by t=x^2+x. The acceleration of the particle is:

1. A. -2/(x+2)^3
2. B. -2/(2x+1)^3 (Correct answer)
3. C. +2/(x+1)^3
4. D. +2/2x+1

Correct Answer

Option B — -2/(2x+1)^3

Detailed Solution & Explanation

The correct answer is Option B.

Key Points

• $t=x^2+x\Rightarrow \dfrac{dt}{dx}=2x+1$, so velocity $v=\dfrac{dx}{dt}=\dfrac{1}{2x+1}$.
• $\dfrac{dv}{dx}=\dfrac{-2}{(2x+1)^2}$.
• Acceleration $a=v\dfrac{dv}{dx}=\dfrac{1}{2x+1}\cdot\dfrac{-2}{(2x+1)^2}=-\dfrac{2}{(2x+1)^3}$.