Question

find displacement from \[0\le t \le 4\]
a(t)=t-5
v(0)=4

Answer 1

\[s''(t)= a(t)\]
so\[s(t)=\int\limits \int\limits a(t)\]

Answer 2

\[
a(t)=t-5\\
v(t)=\int a(t)dt=\int(t-5)dt\\
v(t)={t^2\over2}-5t+c\\
\text{from the fact} \;v(0)=4,c=4\\
v(t)={t^2\over2}-5t+4\\
s=\int_0^4v(t)dt\\
s=\int_0^4\left({t^2\over2}-5t+4\right)dt
\]

Answer 3

now i do the integral of this?

Answer 4

yes

Answer 5

Don't I have to take it between two points as well?
\[\int\limits_{0}^{.876}\int\limits_{.876}^{4}\]

Answer 6

???
where did you get the 0.876 from?

Answer 7

and the two integrals?

Answer 8

nvm idk if i'm even asking the question right.