Calculus Mock Exam Practice Question

Question

For t ≥ 0, a small squirrel moves horizontally along a power line (modeled by the x-axis). The velocity of the squirrel at time t is given by v(t) = 1 + 2sin((t^2)/2). The squirrel is 2 feet to the right of (x=2_ of a main power pole when t =4.

the position of the squirrel relative to the main power pole when t = 0.

Find the total distance that the squirrel travels from time t = 0 to time t =3.

Answer 1

x(0) = x(4) - ∫₀⁴ v(t) dt (with x(4) = 2 given)

total dist = ∫₀³ |v(t)| dt