You run straight off a high diving board at a speed of 6 m/sec. you hit
the water 2 seconds later.
a. how far did you travel horizontally during the 2 seconds?
b. how far did you travel vertically during the 2 seconds?
c. how fast were you moving horizontally when you hit the water?
d. how fast were you moving vertically when you hit the water?

a). Your horizontal speed doesn't change. 
Your horizontal distance is . . .

         (speed) x (time) = ( 6 m/s ) x ( 2s ) = 12 meters .
 
b). Your vertical motion is accelerated because of gravity.
Your vertical distance is . . .

  (original vertical speed x time) + (1/2) (acceleration of gravity) (time)²

  =      ( 0 )                          + (1/2) (9.81) (2)²

  =      4.905 x 4  =  19.62 meters  (a very high diving board indeed, like 64-ft !)
 
c). Your horizontal speed doesn't change. 
It's still 6 m/s when you splash down.
 
d). Your vertical speed grows steadily, because of gravity.
It becomes 9.81 m/s greater every second.

After 2 seconds, your vertical speed is (2 s) x (9.81 m/s²) = 19.62 m/s downward