2)
a) v = ds/dt, a = dv/dt, i assume he knows how to differentiate polynomials.
b) probably best to sketch them in reverse order. a(t)=2t-16 is just a line so that's easy. v(t) is a quadratic with obvious roots (2 and 14) and one turning point (where a is 0, ie t=8), so sketch it from this. then, as in the question in the OP, s is a cubic with positive leading coefficient and you know its turning points so sketch it based on these.
c) it is speeding up when a>0, so t > 8. slowing down when a < 0, so t < 8.
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http://speeddemosarchive.com/MetroidPrime.html#PAL100