A particle is moving with the given data. Find the position of the particle, s(t).

Question

A particle is moving with the given data. Find the position of the particle, s(t).

(i) a(t) = 2t + 7 , s(0) = 3 , v(0) = -3

s(t) = ??

(ii) t^2 - 5t + 4 , s(0) = 0 , s(1) = 20

s(t) = ??

Answer 1

a = 2t +7

v = t^2 + 7t -3

s = t^3/3 +7t^2/2 -3t

if a=t^2-t+4

v = t^3/3 -t^2/2 +4t + c

s =t^4/12 -t^3/6 +2t^2 + ct

s(1) = 1/12 -1/6 +2 + c= 20

c=18 1/12

s(t) = t^4/12 - t^3/6 +2t^2 +217t/12

v= the integral of a

s = the integral of v

s = the double integral of a