The path of motion of a 8-lb particle in the horizontal plane is described in terms of polar coordinates as r = (2 t + 1)ft and θ = (0.2 t2 − t) rad, where t is in seconds.

Missing question in the text:
"Determine the magnitude of the resultant force acting on the particle when t=2s."

For Newton's second law, the force is given by

where m is the mass of the particle and a its acceleration.

The acceleration in polar coordinates is given by:

where


are the radial and tangential accelerations.

Therefore, to find the acceleration starting from the polar coordinates, we need to find the derivatives of r and . Let's compute them:



We need the values at t=2s, therefore we have




and 



And using t=2s,




And now we can calculate the acceleration:


and

And using the mass: 

we find the force: