Step-by-step explanation:
speed (or velocity) = distance/time interval = d/t
acceleration = distance/time interval/time interval =
= d/t²
in such situations (when something is moving or changing fast) we often look for the rates "per second".
therefore,
d/s and d/s²
acceleration is simply the
change of speed/time interval = d d/t / dt
in other words, it builds an arithmetic sequence adding the acceleration amount as constant speed difference for every term of the sequence (= e.g. every second) :
an = a1 + acceleration×n
in physics this is then simply renamed to the first equation of motion :
v = u + at
"v" is the velocity (an) after "t" time units (n) with acceleration "a" after a starting speed "u" (a1).
in our case now, the acceleration adds 100 rad/s speed every second the acceleration applies (2 seconds in our case). starting with 0 rad/s.
if you understand all that, you surely know the result to that question right away, but formally this looks like
v = u + at = 0 + 100×2 = 200 rad/s
the ball's final angular velocity is 200 rad/s.
FYI : the difference between speed and velocity is here irrelevant. they are both measured with the same units anyway.
speed just applies to a current, local movement, while velocity applies to a journey from A to B with (usually) twists and turns along the road and describes the overall mean "speed" along the direct line of sight between A and B.