A 50-kg block is placed on an inclined plane whose angle with the horizontal is 25◦. The viscous friction coefficient between the block and the plane is c = 6 N ·s/m. (a) Derive the equation of...

A 50-kg block is placed on an inclined plane whose angle with the horizontal is 25◦. The viscous friction coefficient between the block and the plane is c = 6 N ·s/m. (a) Derive the equation of motion. (b) Solve the equation of motion for the speed v(t) of the block, assuming that the block is initially given a speed of 5 m/s. (c) Find the steady-state speed of the block and estimate the time required to reach that speed. (d) Discuss the effect of the initial velocity of the steady-state speed.