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CGP EDU Academic Team
Published on: September 12, 2026
The displacement \vec{r} of a particle varies with time t,x = ae^{rt} + be^{st} , where a, b, r and j; are positive constants. The velocity of the particle will
Text Solution
Verified by ExpertsThe correct answer is:
D
\(x = ae^{-i\omega t} + be^{i\omega t}\)
Velocity \(v = \frac{dx}{dt} = \frac{d}{dt} \left( ae^{rt} + be^{st} \right)\)
= a e^{-r^*}(-r^*) + b e^{r^*} r^* = - a r e^{-st} + b r e^{st}
Acceleration \(= -a \mathrm{e}^{-nt}(-t + b) \mathrm{e}^{tr} y_j\)
\(= a r c^{2} e^{-i \omega t} + b p^{2} e^{i \omega t}\)
Acceleration is positive so velocity goes on increasing with time.
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