students in a lab are doing experiments involving the motion of objects. they pull an object across a table and use a detector t
o measure the acceleration of the object for the entire time they pull it. The graph shows the data from the detector, with four segments labeled 
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The impulse (the variation of momentum of the ball) is related to the force applied by
where
is the variation of momentum, F is the intensity of the force and 
is the time of application of the force.
Using F=1000 N and
, we can find the variation of momentum:
This can be rewritten as
where
and 
are the final and initial momentum. But the ball is initially at rest, so the initial momentum is zero, and
from which we find the final velocity of the ball:
where
Using F=1000 N and
This
where
from which we find the final velocity of the ball: