A particle is moving with the given data. Find the position of the particle.
a(t) = t2 − 2t + 7, s(0) = 0, s(1) = 20
s(t)=
+33653 Acceleration: a(t) = t^2 - 2t + 7
Velocity: v(t) = t^3/3 - t^2 + 7t + k1 where k1 is a constant
Position: s(t) = t^4/12 - t^3/3 + 7t^2/2 + k1t + k2 where k2 is another constant
Since s(0) = 0 we have 0 = k2 immediately.
Since s((1) = 20 we have 20 = 1/12 - 1/3 + 7/2 + k1
Hence: k1 = 20 - (1 - 4 + 42)/12 → 20 - 39/12 → 20 - 3 - 1/4 → 67/4
So: s(t) = t^4/12 - t^3/3 + 7t^2/2 + 67t/4
