Answer:
7.3025850929
Step-by-step explanation:
v(t)=(2t)/(1+t^2)
To find the position we need to integrate the function
p(t) = ∫ v(t)
p(t) =∫(2t)/(1+t^2) dt
Using u substitution
u = 1+t^2
du =2t dt
p(t) =∫(du)/(u)
We know that the integral of 1/u du is ln |u|
p(t) = ln|u| +C
Substituting back for u
p(t) = ln|1 +t^2| +C
To find the value of C, we let t=0
p(0) = ln|1 +0| +C = 5
= ln(1) +C =5
0 +C =5 Therefore C=5
p(t) = ln|1 +t^2| +5
We want to find the position at t=3
p(3) = ln|1 +3^2| +5
= ln(10) +5
=7.3025850929
