AP EAMCET · PHYSICS · Motion In One Dimension
A particle is moving along \(X\)-axis with velocity \(v=e^{-\beta x}\). At time \(t=0\), the particle is located at \(x=0\). The displacement of the particle as function of time is
- A \(e^{-\beta t}\)
- B \(\frac{1}{\beta} e^{(1-\beta t)}\)
- C \(\frac{1}{\beta} \log [1-\beta t]\)
- D \(\frac{1}{\beta} \log [1+\beta t]\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{\beta} \log [1+\beta t]\)
Step-by-step Solution
Detailed explanation
Velocity of particle, \(v=e^{-\beta x}\) \(\Rightarrow \quad \frac{d x}{d t}=e^{-\beta x}\) or \(\quad \frac{d x}{e^{-\beta x}}=d t\) or \(\quad e^{\beta x} d x=d t\) \(\Rightarrow\) Integrating, we get \(\int_0^x e^{\beta x} d x=\int_0^t d t\)…
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