A particle is moving with acceleration a ( t ) = 6 t + 16 . its position at time t = 0 is s ( 0 ) = 14 and its velocity at time t = 0 is v ( 0 ) = 6 . What is its position at time t = 7 ?

Question

I need the answer and work please, thank you.

Answer 1

velocity V(t) = integral A(t) dt = integral [ 6t+16] = 3t^2 + 16t + C

initial velocity v(0) = 6 ---> C = 6 , so v(t) = 3t^2 + 16t + 6

position s(t) = integral V(t) dt = integral ( 3t^2 + 16t + 6) = t^3 + 8t^2 + 6t + C

initial position s(0) = 14 ---> C = 14

s(t) = t^3 + 8t^2 + 6t + 14

s(7) = 7^3 + 8(7)^2 + 6(7) + 14

= 343 + 8*48 + 6(7) + 14

= 343 + 384 + 42 + 14

= 727 + 56

= 783