Question

1.A particle is moving along the x-axis with velocity, v(t) = sin2t, t > 0. At time t=pi/2 position x = 3. . Find the total distance, s traveled by this particle on the interval 0<=t<=pi

Answer 1

let s(t) be the displacement function.

remember that the velocity function is the first derivative of the displacement function.

\[v(t) = \frac{ ds }{ dt }\]

we are looking for:\[s(t) = \int\limits_{}^{}v(t) + C\]

Answer 2

C is found by plugging s(pi/2) = 3

Answer 3

if you want we can look at s(t) as x(t) [a bit more appropriate for this problem]