WBJEE · Physics · Motion In One Dimension
A particle is travelling along a straight line \(O X\). The distance \(x\) (in metre) of the particle from 0 at a time t is given by \(x=37+27 t-t^{3}\), where t is time in seconds. The distance of the particle from \(O\) when it comes to rest is
- A \(81 \mathrm{m}\)
- B \(91 \mathrm{m}\)
- C \(101 \mathrm{m}\)
- D \(111 \mathrm{m}\)
Answer & Solution
Correct Answer
(B) \(91 \mathrm{m}\)
Step-by-step Solution
Detailed explanation
Given, \(x=37+27 t-t^{3}\) \[ v=\frac{d x}{d t}=27-3 t^{2} \] According to problem, \[ v=0 \Rightarrow 27-3 t^{2}=0 \] Here, \(t=3 \mathrm{s}\) \[ x=37+27 \times 3-(3)^{2}=91 \mathrm{m} \]
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