AP EAMCET · Maths · Application of Derivatives
If the velocity of a particle moving on a straight line is proportional to the cube root of its displacement, then its acceleration is
- A constant
- B inversely proportional to its velocity
- C proportional to its velocity
- D proportional to its displacement
Answer & Solution
Correct Answer
(B) inversely proportional to its velocity
Step-by-step Solution
Detailed explanation
\( v = k x^{1/3} \) \( \frac{dv}{dx} = \frac{k}{3} x^{-2/3} \) \( a = v \frac{dv}{dx} = (k x^{1/3}) (\frac{k}{3} x^{-2/3}) = \frac{k^2}{3} x^{-1/3} \) \( x^{-1/3} = (x^{1/3})^{-1} = (v/k)^{-1} = k/v \) \( a = \frac{k^2}{3} \frac{k}{v} = \frac{k^3}{3v} \) acceleration is…
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