## anonymous one year ago The velocity in ft/sec of a particle is given by v(t) = −16t + 2. Find the position function s(t), of the particle if it has an initial position s(0) = 6 feet.

1. anonymous

@jim_thompson5910

2. anonymous
3. jim_thompson5910

integrate v(t) to get s(t) don't forget the +C. You'll solve for C by using s(0) = 6

4. jim_thompson5910

s(0) = 6 means x = 0 and y = 6

5. anonymous

Is it A? How would you relate v(t) to s(0)

6. jim_thompson5910

you can always check by deriving back

7. jim_thompson5910

y = -16t^2 + 2t + 6 dy/dt = -32t + 2 which is not the same as v(t)

8. anonymous

D?

9. jim_thompson5910

$\Large s(t) = \int v(t)dt$ $\Large s(t) = \int (-16t + 2)dt$ You should find that s(t) = -8t^2 + 2t + C s(t) = -8t^2 + 2t + C s(0) = -8*0^2 + 2*0 + C s(0) = C 6 = C C = 6 So, s(t) = -8t^2 + 2t + 6. Yep it's definitely D