i need calc help
A particle is moving with acceleration a(t)=36t+2. its position at time t=0 is s(0)=10 and its velocity at time t=0 is v(0)=12. What is its position at time t=6?

Question

i need calc help
A particle is moving with acceleration a(t)=36t+2. its position at time t=0 is s(0)=10 and its velocity at time t=0 is v(0)=12. What is its position at time t=6?

anonymous · Answer

integrate a(t) ?

anonymous · Answer

so that would be a(t) = 18t^2+2x

anonymous · Answer

if you integrate acceleration you get velocity

anonymous · Answer

v(t) = 18t^2+2t + constant

anonymous · Answer

So then i would plug in 0 into x and solve for c giving me the value of 12?

anonymous · Answer

yes

anonymous · Answer

if you integrate velocity you get position

anonymous · Answer

so 6s^3+t^2+12x+c then i plug in 0 to give me c = 10 so...

6s^3+t^2+12t+10 = position?

anonymous · Answer

awesome i got it. thanks!