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.

Question

anonymous · Answer

@jim_thompson5910

anonymous · Answer

https://gyazo.com/d72329de0e37c8a6350e14c0d14a05b5

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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

anonymous · Answer

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

jim_thompson5910 · Answer

you can always check by deriving back

jim_thompson5910 · Answer

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

anonymous · Answer

D?

jim_thompson5910 · Answer

$$\Large s(t) = \int v(t)dt$$
$$\Large s(t) = \int (-16t + 2)dt$$
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