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You are told that a basketball player spins the ball with an angular acceleration of 100 rad/s². What is the ball’s final angular velocity if the ball starts from rest and the acceleration lasts 2.00 s?

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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.

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