The velocity of the truck can be determined using velocity equation in polar coordinates,

     
where
     

     v = 0.0889t e_r + 14(0.0500) e_θ

However, this is still a function of t. To find the time time t required for the truck to travel from r = 4 to r = 14 meters, integrate the radial component of the velocity, giving

     (0.0889 t²)/2 = 14 - 4

     t = 15 s

Now, substitute t into the equation to calculate the final velocity, v,

Acceleration Motion

Similarly, the acceleration equation can be used to calculate the acceleration of the truck when it is 14 meters from the center of the carousel. Since the time has already be determined previously, no integration is required.

     
where
     

     a = [0.0889 - 14(0.0500)²]e_r
                           + [2(0.0889)(15)(0.0500) - 0]e_θ

     a = 0.5390e_r + 0.1334e_θ