Question

The motion of a body is given by $\frac{dv}{dt}=6-3v$ where $v$ is the velocity (in $m{s}^{-1}$) at a time $t$ (in seconds). The body is at rest at t = 0. The terminal speed of the body is

• A. $1m{s}^{-1}$
• B. $2m{s}^{-1}$
• C. $3m{s}^{-1}$
• D. $6m{s}^{-1}$

Answer 1

The correct option is B

$2m{s}^{-1}$

The acceleration is given by
$a=\frac{dv}{dt}=6-3v........\left(i\right)$
The terminal speed $v_1$ is the speed when the acceleration is zero.
Using a = 0 in equation (i), $0=6-3v_1$
$\Rightarrow v_1=2m/s$
Hence, the correct option is (b).