math

A particle is traveling along a one-dimensional path (such as a number line). The position of the particle is
governed by the time function x(t) ƒ­ 3t 4 ƒ{16t3 ƒy18t 2 ƒy 2 , where t is in minutes and 0 „T t „T 5 . Answer the
following questions.
a) At what times is the particle stationary?
b) For which time intervals is the particle moving in a positive direction? A negative direction?
c) What is the particle¡¦s most positive position? Most negative position?
d) What is the particle¡¦s displacement? What is the total distance the particle has traveled?
e) When does the particle¡¦s acceleration undergo a sign change? What is the particle¡¦s acceleration at the
times when the particle is stationary?
f) Sketch a graph (on a t-x coordinate plane) of the particle¡¦s position using the information above.

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