Question
The most economical speed to run the train is
✓
Answer
We have, $\frac{d C}{d v}=\frac{375}{4}-\frac{600000}{v^2}$
Put $\frac{d C}{d v}=0 \Rightarrow v^2=\frac{600000 \times 4}{375}=6400$
$\Rightarrow v=80 km / h$
$
\frac{d^2 C}{d v^2}=\frac{2 \times 600000}{v^3}>0 \text {, for } v=80
$
$\therefore$ Most economical speed is $80 km / h$.
Put $\frac{d C}{d v}=0 \Rightarrow v^2=\frac{600000 \times 4}{375}=6400$
$\Rightarrow v=80 km / h$
$
\frac{d^2 C}{d v^2}=\frac{2 \times 600000}{v^3}>0 \text {, for } v=80
$
$\therefore$ Most economical speed is $80 km / h$.
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