Answer
(a)
$\dfrac{dV}{dv}=-1$
(b)
$\dfrac{dV}{dt}=-4$
Work Step by Step
(a)
Given $V=-Blv$.
This gives $\dfrac{dV}{dv}=\dfrac{d}{dv}(-Blv)$.
Since it is a linear form with variable $v$ and constants $B$ and $l$.
$\dfrac{dV}{dv}=-Bl$
Substitute $B=2$ and $l=0.5$ and simlify.
$\dfrac{dV}{dv}=-2\times 0.5=-1$
Hence, $\dfrac{dV}{dv}=-1$
(b)
Firstly, find the rate of change of velocity with respect to time.
We have given $v(t)=4t+9$.
This gives $\dfrac{dv}{dt}=\dfrac{d}{dt}(4t+9)=4$.
Now multiply $\dfrac{dv}{dt}$ on both side of $\dfrac{dV}{dv}=-1$ and simplify.
We get $\dfrac{dV}{dv}\dfrac{dv}{dt}=-1\dfrac{dv}{dt}$.
On simplification we get $\dfrac{dV}{dt}=-1\dfrac{dv}{dt}=-4$.
