Dynamics of Particles and Rigid Bodies Spring 2023 is the position of P expressed in terms of the arc length, and c is a constant. Extra Credit. [10 pts] The particle P is traveling on a circular path with radius r from point A to point B in the counterclockwise direction, as depicted in Fig. 4. Its motion can be described by s(t) = ct where s a) [1 pt] Determine the speed v(t) of the particle P as a function of time t. function of time t, and eliminate to express v(t) in terms of c, t, and r. b) [2 pts] Use the result found in Part a) to determine the velocity (vector) v(t) of the particle P as a P when it reaches point B. d) [2 pts] Use the results found in Parts b) and c) to determine the velocity (vector) v(tB) of the particle c) [2 pts] Determine the time to required for the particle P to travel from point A to point B. e) [1 pt] Use the result found in Part a) to determine the tangential acceleration a, of the particle P. particle P expressed in terms of c, s, and r. f) [2 pts] Use the result found in Part a) to determine the normal (centripetal) acceleration an of the y B 0 P r S A Figure 4: A particle P traveling on a circular path from A to B.