Answer to Question #186297 in Mechanical Engineering for Saad

Question #186297

The velocity of a particle which moves along the strait line with a velocity which is given in millimeter per second given by S= 4220t3- 116t2+ 45t-17, where t is in second. Calculate the Velocity and acceleration of a particle? if t= 3sec and t= 5sec then find out he value of a and v ?


1
Expert's answer
2021-05-05T07:41:32-0400

Average velocity = S / t = Vavg

Displacement, S = vdt = (4220t3 - 116t2 + 45t - 17)dt = 4220 t4/4 - 116 t3/3 + 45 t2/2 - 17t = (4220 x 54/4 - 116 x 53 / 3 + 45 x 52 / 2 - 17 x 5) - (4220 x 34/4 - 116 x 33 / 3 + 45 x 32 / 2 - 17 x 3) = 655019 - 84563 = 570 456 m

Vavg = 570 456 m / 2 sec = 285 228 m/s

Average acceleration aavg = (Vf - Vi) / t

Vf = 4220 x 53 - 116 x 52 + 45 x 5 - 17 = 524 808

Vi = 4220 x 33 - 116 x 32 + 45 x 3 - 17 = 113 014

aavg = (524 808 - 113 014) / 2 = 205 897 m/s2

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