Calculus Question

Question

A particle moving along the x-axis with velocity at time t given by v(t) = 1 + 2cos√t.

The position is not given, but the position at time t = 1 is -3.

a) What is the position of the particle at time t=6?

b) What is the total distance traveled by the particle from t = 0 to t=4?

Answer 1

v = 1 + cos(sqrt)

s = t + -sin(sqrt)[1/2t^2) + c where c=an unknown constant term

s(1)=-3 = 1 - sin(1)/2 + c

c = .5sin1 -4

s(t) = t -.5sin(sqrt)(1/2t^2) + .5sin1 -4

s(6)= 6 - .5sin(sqr6)/(1/72) + .5sin1 - 4

distance traveled from 0 to 4 = s(4)-s(0)

s(0) is undefined

= 2 -.(1/360)sin(sqr6) +(sin1)/2