If 4 wands are equivalent to 6 rands and 24 rands are equivalent to 8 fands, how many wands are equivalent to 5 fands?
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a) Acceleration is the derivative of velocity. By the fundamental theorem of calculus,
so that
b) We get the displacement by integrating the velocity function like above. Assume the object starts at the origin, so that its initial position is . Then its displacement over the time interval [0, 3] is
c) The total distance traveled is the integral of the absolute value of the velocity function:
for
and
for
, so we split the integral into two as