The position of a particle moving along an x axis is given by x = 11t2 - 6.0t3,

Question

The position of a particle moving along an x axis is given by x = 11t2 - 6.0t3, 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?
xmax = m
At what time is it reached?
t =____ s

(c) What is the maximum positive velocity reached by the particle?
vmax = m/s
At what time is it reached?
t =___ 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



THANK YOU!!!!!!!!!!

Explanation / Answer

x = 11t2 - 6.0t3 =11*3^2-6*3^3 =-63m dx/dt=22t-18t^2 since,dx/dt=v v=22t-18t^2 =22*3-18*3^2 putting t=3 sec =66-18*9 =-96m/sec dv/dt=22-36t =22-36*3 =-86m/sec^2 b)max positive coordinaate is reached at time t=11/9s c)t=11/18 d)22m/s2 e)48m/s

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