The displacement \vec{r} of a particle varies with time t_x = ae^x + be^{-x} , where a, b, r and j; are positive constants. The velocity of the particle will
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\(x = ae^{-i\omega t} + be^{i\omega t}\)
Velocity \(v = \frac{dx}{dt} = \frac{d}{dt} (ae^{-rt} + be^{rt})\)
\(= a.e^{-i\omega t}(-r(x) + b e^{i\omega t} . f(x))\) = - a r e^{-st} + b r e^{st}
Acceleration \(= - a \mathrm{re}^{-i \pi} (-i t) + b) j e^{t r} , j j\)
\(= a r c^{2} e^{-i \omega t} + b p^{2} e^{i \omega t}\)
Acceleration is positive so velocity goes on increasing with time.
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