SOLUTION: What is the set up to the word problem As a particle moves along a straight path, its speed "v"(in cm/sec0 at time "t"(in seconds) is given by the equation below. For what subinter
Algebra.Com
Question 103299: What is the set up to the word problem As a particle moves along a straight path, its speed "v"(in cm/sec0 at time "t"(in seconds) is given by the equation below. For what subintervals of the time interval [0,6] will its speed be at least 14cm/sec?
v=t^3-4t^2-9t+50
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
As a particle moves along a straight path, its speed "v"(in cm/sec0 at time "t"(in seconds) is given by the equation below. For what subintervals of the time interval [0,6] will its speed be at least 14cm/sec?
v=t^3-4t^2-9t+50
----------------------
Solve t^3-4t^2-9t+50 >= 14
t^3 -4t^2 -9t + 36 >= 0
(t+3)(t-3)(t-4) >= 0
-------------------------
Draw a number line.
Mark the numbers -3, 3, 4
These are solutions for EQUALITY.
------------------------------
Check a value from each interval to find solutions for the INEQUALITY:
In (-inf,-3), let t=-4 to get: -*-*- <0 so no solutions
-------------------------
In (-3,3), let t=2 to get: +*-*- >0 so solutions in that interval
-------------------------
In (3,4), let t=3.5 to get: +*+-<0 so no solutions
-------------------------------------
In (4,+inf), let t=5 to get: +*+*+>0 so solution in that interval
----------------------------------
Solution: [-3,3] U [4,+inf)
===============================
Cheers,
Stan H.
RELATED QUESTIONS
As a particle moves along a straight path, its speed v (in cm/sec) at time t (in... (answered by stanbon)
A particle moves in a straight line so that its velocity v m/s is given by v=9-t^2,where... (answered by ikleyn)
A particle moves in a straight line so that its velocity v m/s is given by v=9-t^2,where (answered by ikleyn)
An object moves along a straight path at a speed v(t) = 4t^2 + 3t + 2 in m/s, where t =... (answered by Alan3354)
Please help me with this problem:
A particle moves along the x axis so that its velocity (answered by Fombitz,robertb)
A particle moves in a straight line with velocity v(t)=root(3t-1) metres per second where (answered by math_tutor2020)
A particle moves in a straight line with velocity v(t)=r00t(3t-1)metres per second where... (answered by math_tutor2020)
A particle moves in a straight line with velocity V(t)=root(3t-1) meters per second where (answered by CPhill)
An object moves along a straight path at a speed v(t) = 2+4t-t2 of m/s. When will the... (answered by ikleyn)