Dynamics of Rigid Bodies

. . Dynamics of Rigid Bodies. Tumamao, Roselyn Joy M. Montoya, Ralph Roger G..

. . Quiz 1. Solutions. Solutions for numbers 1-5.

. . 1. The velocity of a particle is given by v = 20t2 - 1 00t + 50, where v is in meters per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 6 seconds of motion and evaluate the velocity when a is zero..

. 2. The displacement of a particle is given by s = 2t3 - 30t2 + 1 00t - 50, where s is in feet and t is in seconds. Plot the displacement, velocity and acceleration as functions of time for the first 1 2 seconds of motion. Determine the time at which the velocity is zero..

. 3. The position of a particle in millimeters is given by s = 27 - 12t + t2, where t is in seconds. Plot the s-t and v-t relationship for the first 9 seconds. Determine the net displacement As during that interval and the total distance D traveled. By inspection of the s-t relationship, what conclusion can you reach regarding the acceleration?.

. . 4. The acceleration of a speed boat starting from rest is described by the graph. Construct the v-s graph. Solution:.

. . න. 48.99??/?. 4. ??? = න. 200 ??. 5. 10??.

. 5. The boat travels in a straight line with the acceleration described by the a-s graph. If it starts from rest, construct the v-s graph and determine the boat’s maximum speed. What distance s’ does it travel before it stops? Solution: ??????? ???????? ?? ?ℎ? ???? : ? = 150? Vmax = ? | s=50m = (−0.02 1502 + 12(150) Vmax = 36.74 m/s 150 < ? < ? ′ ; ? = 36 . 74 ? ? ?? ? = 150 ??? = ??? න 36.74 ?/? ? ??? = න 150 ?? ? −4?? ? = ( − 85 + 2550 ) ? / ?.

. ? = 0 0 = − 85′ + 2550 ) ?′ = 318 . 75? ? − ? ????ℎ 0 ≤ ? < 150? ; ? = 0 ?? ? = 0 ??? = ??? න 0 ? ??? = න 0 15 −0.02 + 6 ?? ? = − 0 . 02? 2 + 12? ? / ?.