The motion of a body is given by the equation d`nu`/dt = 6 - 3`nu` where `nu` is the speed in `m s^(-1)` and t is time in s. The body is at rest at t = 0. The speed varies with time asA. `nu = (1 - e^(-3t))`B. `nu = 2(1 - e^(-3t))`C. `nu = 1 + e^(-2t)`D. `nu = 2(1 + e^(-2t))`

The motion of a body is given by the equation d`nu`/dt = 6 - 3`nu` whe

1.	The motion of a body is given by the equation d`nu`/dt = 6 - 3`nu` where `nu` is the speed in `m s^(-1)` and t is time in s. The body is at rest at t = 0. The speed varies with time asA. `nu = (1 - e^(-3t))`B. `nu = 2(1 - e^(-3t))`C. `nu = 1 + e^(-2t)`D. `nu = 2(1 + e^(-2t))`
Answer» Correct Answer - B `(dv)/(dt) = 6 - 3v` or `(dt) = (dv)/(6 - 3v)` Integrating both sides, we get `t = 1/3 ln(6 - 3v) + C` where C is a constant of integration At t = 0, v = 0 `therefore` `C = 1/3 ln 6` `therefore = -1/3 ln(6 - (3v)/(6)` or `e^(-3t) = 1 - 1/(2 v)` or `v = 2(1 - e^(-3t))`

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The motion of a body is given by the equation d`nu`/dt = 6 - 3`nu` where `nu` is the speed in `m s^(-1)` and t is time in s. The body is at rest at t = 0. The speed varies with time asA. `nu = (1 - e^(-3t))`B. `nu = 2(1 - e^(-3t))`C. `nu = 1 + e^(-2t)`D. `nu = 2(1 + e^(-2t))`

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