Answer to Question #186297 in Mechanical Engineering for Saad

Question

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 ?

Answer 1

Average velocity = S / $\Delta$t = V_avg

Displacement, S = $\int$ vdt = $\int$ (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

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

Average acceleration a_avg = (V_f - V_i) / $\Delta$t

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

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

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