WBJEE · Maths · Application of Derivatives
The displacement of a particle at time \(t\) is \(x\), where \(x=t^4-k t^3\). If the velocity of the particle at time \(t=2\) is minimum, then
- A \(\mathrm{k}=4\)
- B \(\mathrm{k}=-4\)
- C \(\mathrm{k}=8\)
- D \(\mathrm{k}=-8\)
Answer & Solution
Correct Answer
(A) \(\mathrm{k}=4\)
Step-by-step Solution
Detailed explanation
Hints : \(\frac{d x}{d t}=4 t^3-3 k t^2\) \(\frac{d v}{d t}=12 t^2-6 \mathrm{kt}\) at \(\mathrm{t}=2\) \(\Rightarrow \frac{\mathrm{dv}}{\mathrm{dt}}=0,48-12 \mathrm{k}=0 \quad ; \mathrm{k}=4\)
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