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.

Explanation / Answer

a) t=3 x=17*9-5*27 =18 v=dx/dt=34t-15t^2 =34*3-15*9 =-33 a=dv/dt =34-30t =34-90 =-56 b) dx/dt=0 t=34/15 x=17*(34/15)^2-5*(34/15)^3 =29.11 c) dv/dt=0 t=34/30 v=34*34/30-15*(34/30)^2 =19.27

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