Motion-related Problems
Motion with constant velocity
The distance traveled is the product of velocity and time.
$s = vt$
were,
s = distance
v = velocity
t = time
It follows that
$t = \dfrac{s}{v}$ and $v = \dfrac{s}{t}$
Motion in a current of water or air
Let
x = velocity of the (boat/airplane) in still (water/air) and
y = velocity of the (water/air), then
x + y = velocity when going (downstream/with the wind)
x - y = velocity when going (upstream/against the wind)
Motion in a circle or any closed circuit
Consider two objects, one is a faster and the other is slower, moves from the same point and starting at the same time.
- When going in the same the direction, the difference of the distances traveled every time the faster overtakes the slower is one circuit.
$s_{faster} - s_{slower} = 1 \text{ circuit}$ - When going in opposite directions, the total distance traveled every time the two meet each other is one circuit.
$s_{faster} + s_{slower} = 1 \text{ circuit}$