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

     

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