A particle is moving with the given data. Find the position of the particle.
a(t) = t^2 − 2t + 6, s(0) = 0, s(1) = 20
Assuming a(t) is acceleration, then
velocity is: v(t) = t3/3 - t2 + 6t + k1 where k1 is a constant
position is: s(t) = t4/12 - t3/3 + 3t2 + k1t + k2 where k2 is another constant.
The two constants are found from:
s(0) = 0: 0 = k2
s(1) = 20: 20 = 1/12 - 1/3 + 3 + k1 + k2