Question

The position of a particle moving along the x-axis for any time, t> 0, is given by s(t) = - cos^2 (2t) + ln(t) + e ^ sin(t) where s(t) is measured in inches and t is measured in seconds.

Find the velocity of the particle at t = 8 seconds.

Answer 1

s(t) = - cos^2 (2t) + ln(t) + e ^ sin(t)
now just use the chain rule to find
v(t) = -2cos(2t)*(-sin(2t))*2 + 1/t + e^sint * cost
now find v(8)