The position of a particle moving along an x axis is given by x = 17t2 - 5.0t3,

Question

The position of a particle moving along an x axis is given by x = 17t2 - 5.0t3, where x is in meters and t is in seconds. (a) Determine the position, velocity, and acceleration of the particle at t = 3.0 s. x = ____m v = ____m/s a = ____m/s2 (b) What is the maximum positive coordinate reached by the particle? ____m At what time is it reached? _____s (c) What is the maximum positive velocity reached by the particle? m/s At what time is it reached? _____s (d) What is the acceleration of the particle at the instant the particle is not moving (other than at t = 0)? _____m/s2 (e) Determine the average velocity of the particle between t = 0 and t = 3 s. _____m/s

Explanation / Answer

a) x = 17t^2 - 5 t^3 v = 34 t - 15 t^2 a = 34 - 30 t at t=3s x= 17*3^2 - 5*3^3=18 v=34*3-15*9=-33 a = 34-30*3=-56 b) max when v= 0 v=0 at t= 0 or t =34/15 t=34/15 is maximum x = 29.11 c) max velocity when a = 0 at t= 34/30 v = 19.27 d) a = 34 -30*34/15=-34 e) v average = (xf - xi)/t = 18-0/3 = 6

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