Since displacement can be connected to motion, a train rapidly leaving shows a change in position.
Common equations used with motion problems
Where....
is the body's initial velocity
is the body's initial position
, The velocity at the end of the interval
, the position at the end of the interval
, the time interval between the initial and current states
, the constant acceleration, or in the case of bodies moving under the influence of gravity
(Note: Graphs and their slopes do not correlate with each other.)
What do the slopes mean?
displacement-time graph-velocity
velocity-time graph-acceleration
acceleration-time graph-meaningless
Seen here is a picture of Niagara Falls. In the picture, the speed of the water is increasing rapidly as it falls. Since velocity takes into account speed and direction, and the water is moving in a downward direction, the velocity is negative. The water is being accelerated down at a rate of 9.81 m/s/s due to gravity.
You can see a motion problem almost anywhere, like this clip of Wile E. Coyote and Road Runner. Note the time oit takes Wile E. Coyote to fall and see if you can calculate the distance
is the body's initial velocity
is the body's initial position
, The velocity at the end of the interval
, the position at the end of the interval 
, the time interval between the initial and current states 
, the constant acceleration, or in the case of bodies moving under the influence of gravity
