Question

Given: A position of a particle which moves along a straight line is defined by the relation $s = t^3 - 6t^2 - 15t + 40$. where s is expressed in feet and t in seconds Find: a) Or derive the equation of the particle's velocity as a function of time [i.e., $v = f(t)$] b) Or derive the equation of the particle's acceleration as a function of time [i.e., $v = f(t)$] c) The time at which the velocity will be zero. d) The position of the particle when the velocity is zero. e) The acceleration of the particle when the velocity is zero. f) The displacement of the particle from $t = 4$ sec to 6 sec. g) The distance traveled by the particle from $t = 4$ sec to 6 sec.

          Given:
A position of a particle which moves along a straight line is defined by the relation $s = t^3 - 6t^2 - 15t + 40$.
where s is expressed in feet and t in seconds
Find:
a) Or derive the equation of the particle's velocity as a function of time [i.e., $v = f(t)$]
b) Or derive the equation of the particle's acceleration as a function of time [i.e., $v = f(t)$]
c) The time at which the velocity will be zero.
d) The position of the particle when the velocity is zero.
e) The acceleration of the particle when the velocity is zero.
f) The displacement of the particle from $t = 4$ sec to 6 sec.
g) The distance traveled by the particle from $t = 4$ sec to 6 sec.

Given:
A position of a particle which moves along a straight line is defined by the relation s = t^3 - 6t^2 - 15t + 40.
where s is expressed in feet and t in seconds
Find:
a) Or derive the equation of the particle's velocity as a function of time [i.e., v = f(t)]
b) Or derive the equation of the particle's acceleration as a function of time [i.e., v = f(t)]
c) The time at which the velocity will be zero.
d) The position of the particle when the velocity is zero.
e) The acceleration of the particle when the velocity is zero.
f) The displacement of the particle from t = 4 sec to 6 sec.
g) The distance traveled by the particle from t = 4 sec to 6 sec.

Added by Carlos B.

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