1. $a$ km/hr $=\left(a\times \frac{5}{18}\right)$ m/s.
2. $a$ m/s $=\left(a\times \frac{18}{5}\right)$ km/hr.
3. Time taken by a train $A$ of length $l$ metres to pass a telegraph post or standing man is equal to the time taken by the train to cover $l$ metres.
4. Time taken by a train $P$ of length $l$ metres to pass a signal post of length $b$ metres is the time taken by the train to cover $(l + b)$ metres.
5. Suppose two trains, $A$ and $B$ are moving in the same direction at $u$ m/s and $v$ m/s, where $u>v$, then their relative speed is $=(u-v)$ m/s.
6. Suppose two trains $P$ and $Q$ are moving in opposite directions at $u$ m/s and $v$ m/s, then their relative speed is $=(u+v)$ m/s.
7. If two trains of length $x$ metres and $y$ metres are moving in opposite directions at $u$ m/s and $v$ m/s, then:
The time taken by the trains to cross each other $=\frac{(x+y)}{(u+v)}$ sec.
8. If two trains of length $x$ metres and $y$ metres are moving in the same direction at $u$ m/s and $v$ m/s, then:
The time taken by the faster train to cross the slower train $=\frac{(x+y)}{u-v}$ sec.
9. If two bodies start at the same time from points $P$ and $Q$ towards each other and after crossing they take $x$ and $y$ sec in
reaching $Q$ and $P$ respectively, then:
($P$'s speed):($B$'s speed) $=\left(\sqrt{y}:\sqrt{x}\right)$
