Answer:
B=22.348 Inches per minutes
Step-by-step explanation:
A snail is traveling along a straight path. The snail’s velocity can be modeled by [tex]v(t)=1.4ln(1+t^2)[/tex] inches per minute for 0 ≤ t ≤ 15 minutes.
If the snail's velocity is [tex]v(t)=1.4ln(1+t^2)[/tex] per minute, its displacement for 0 ≤ t ≤ 15 minutes is given by the integral:
[tex]\int_{0}^{15}1.4ln(1+t^2)dt=76.04307[/tex]
The ant travels with a constant acceleration of 2 Inches per minute.
Therefore, the velocity of the ant will be:
[tex] \int 2 dt=2t+c,[/tex] inches per minutes, for some constant c.
For the interval, 12≤t≤15, the displacement of the ant is:
[tex] \int_{12}^{15}(2t+c)dt=t^2+ct|_{12}^{15}=81+3c[/tex]
Since the snails displacement and that of the ant are equal in 12≤t≤15.
81+3c=76.04307
3c=76.04307-81
3c=-4.95693
c=-1.65231
The velocity of the ant at t=12 is therefore:
2t+c=2(12)-1.65231=22.348 Inches per minutes
B=22.348 Inches per minutes
