A body is falling freely in a resistive medium. The motion of the body is described by $\frac{dv}{dt} = (4 - 2

Question

A body is falling freely in a resistive medium. The motion of the body is described by $\frac{dv}{dt} = (4 - 2v)$, where $v$ is the velocity of the body at any instant (in $	ext{m s}^{-1}$). The terminal velocity in this case refers to the velocity the body approaches as time $t 	o \infty$. The initial acceleration and terminal velocity of the body, respectively, are:

Accepted Answer

1.  **Analyze the Equation:** The acceleration of the body is given by the derivative of velocity with respect to time: $a = \frac{dv}{dt} = 4 - 2v$ .
2.  **Calculate Initial Acceleration:** 'Falling freely' in this context implies the body starts from rest (dropped) at $t=0$. Thus, initial velocity $v = 0$. Substituting this into the equation:
    $$a_{	ext{initial}} = 4 - 2(0) = 4 	ext{ m/s}^2$$
3.  **Calculate Terminal Velocity:** Terminal velocity ($v_T$) is the constant velocity reached when the resistive force balances the driving force, resulting in zero acceleration. As $t 	o \infty$, $\frac{dv}{dt} 	o 0$. Setting acceleration to zero:
    $$0 = 4 - 2v_T$$
    $$2v_T = 4$$
    $$v_T = 2 	ext{ m/s}$$

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