If the position of a car is given by s=(80/3)[t + (3/pi)sin(pi*t/6)]. Find its velocity.

The velocity is the derivative of distance, with respect
to time:

v = ds/dt

We'll
calculate the derivative:

v = d/dt[(80/3)t + (80/pi)sin
(pi*t/6)]

We'll remove the
brackets:

v = (80/3)(d/dt t) + (80/pi)(d/dt[sin
(pi*t/6)]

v = (80/3) + (80/pi)(pi/6)[cos
(pi*t/6)]

v = (80/3) + (40/3)[cos
(pi*t/6)]

We'll factorize by 40/3 and we'll
get:

v = (40/3)[2 + cos
(pi*t/6)]