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.

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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.

Mathematics
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https://gyazo.com/d72329de0e37c8a6350e14c0d14a05b5
integrate v(t) to get s(t) don't forget the +C. You'll solve for C by using s(0) = 6

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s(0) = 6 means x = 0 and y = 6
Is it A? How would you relate v(t) to s(0)
you can always check by deriving back
y = -16t^2 + 2t + 6 dy/dt = -32t + 2 which is not the same as v(t)
D?
\[\Large s(t) = \int v(t)dt\] \[\Large s(t) = \int (-16t + 2)dt\] 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

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