Answer:
s(4)=450
Explanation:
Given Data
a(t)=30t+8
at t=0 s(0)=14
at t=0 v(0)=13
s(4)=?
Solution
we know v is derivative of a
and s is derivative of v
a(t)=30t+8
derivative it we get
[tex]v(t)=15t^{2}+8t+c\\ put t=0\\v(0)=15(0)^{2}+ 8(0)+c\\v(0)=c\\c=13[/tex]
so
[tex]v(t)=15t^{2}+8t+13[/tex]
derivative it we get
[tex]s(t)=\frac{15}{3}t^{3}+4t^{2}+13t+c\\ t=0\\s(0)=\frac{15}{3}(0)^{3}+4(0)^{2}+13(0)+c\\s(0)=c\\c=14[/tex]
so
[tex]s(t)=\frac{15}{3}t^{3}+4t^{2}+13t+14\\t=4\\s(4)=\frac{15}{3}(4)^{3}+4(4)^{2}+13(4)+14\\s(4)=450[/tex]
