Question

Bookmarks People Window Help 17 100 BD Microsoft Word - CLO 01.docx X + ebdav/pid-13471437-dt-content-rid-22292132_1/courses/DBM_6312/CLO%2001%20-%20HW%20%23%2 Dr. Amjad Saar ME 3 Adams The position of a particle is defined by r = {5 cos 21 i + 4 sin 21 j} m, where is in seconds and the arguments for the sine and cosine are given in radians. Determine the magnitudes of the velocity and acceleration of the particle when t = 1 s. The velocity of a particle is y=(3+ (6 - 20 m/s, where!

Answer 1

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Solution : r= {5 Cosati + 4 Sin 2t j} To find : velocity (v) magnitudes at & Accleration (a). t= 1 sec v= der at - d (5 (as (2t)i + 4 sin(2t j ). de = - 10 sin (at)i + 8 cos (at); (1) at t= 1 sec. V= [ 9.093 i- 3.329 ;] mis . Magnitude : V = V(-9.093) + (-3.329)? - : V = 9.68 m/s V = g. 68 mis

a= dv dt = {-10 Sin (2+); + 8 cod (2+) dt - from Eq? - = -20 cos (2 t) ; - 16 Sin (2+); at t = 1 sec - a= -20 cos (2)i + 16 sin (22) | 8. 323i - 14.549; 3 m/s Magnitude a= √ (8.323) ² + (-14.54g)? a = 16.76 m/s2| Answers : v= a= 9.68 m/s 16.76m 15²