The position of a particle moving along an x axis is given by x = 19t2 - 4.0t3,

Question

The position of a particle moving along an x axis is given by x = 19t2 - 4.0t3, 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=63 m v=6 m/s a=-34 m/s^2 b) 38*t-12*t^2=0 t=3.167 x(max)=63.5 m c)38-24*t=0 t=1.58 sec v(max)=30.08 m/s a(t=1.58)=-24*1.58=-37.92 m/s^2 v(avg)=x(3)-x(0)/3=63/3=21 m/s

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