Calculus homework help Can you help me please?

Question

I have the velocity of v(t)= -t +8 when t is greater than 6 and less than or equal to 11. I need to know the distance function f(t) that corresponds to the v(t).

I also have the velocity of v(t)= 3t-36 when t is greater than 11 and less than or equal to 12. I need to know the distance function f(t) that corresponds to the v(t).

Thanks.

Answer 1

You should have learned that v(t) = ds/dt, where s is the distance.
Since ds/dt = v(t) = -t +8
s(t) = -0.5*t^2 + 8t + c, for 6 < t <= 11
where c + 30 is the value s(6), which you have not specified yet. Similarly,
s(t) = 1.5*t^2 - 36t + C, for 11 < t <= 12
where 216 - 36*12 + C is the value s(12), which you have not specified yet.