A particle is moving along a straight line through a fluid medium such that its speed is measured as v=(2t) m/s, where t is in seconds. If it is released from rest at s=0, determine its positions and acceleration when t=3 s.
We have the velocity so to find the acceleration we derivate the function v
dv/dt = a = 2
So the acceleration is always 2
To find the position all you need to do is integrate the velocity
integral of velocity = s = t2
Then you just plug in the 3 seconds into the equations:
a(3) = 2 m/s2
s(3) = 9 m
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