# 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.

$s_{faster} + s_{slower} = 1 \text{ circuit}$