SOLUTION: The velocity of a particle moving with SHM in a straight line is given by v=4x-x^2. Find the max speed of the particle. The answer is 4m/s but I keep getting 2m/s.

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Question 1142640: The velocity of a particle moving with SHM in a straight line is given by v=4x-x^2. Find the max speed of the particle.
The answer is 4m/s but I keep getting 2m/s.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!



max at

=>->disregard
=>
answer is
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

You are given


    V(x) = 4x - x^2 = x*(4-x).


The roots of this parabola are x= 0 and x= 4 -- hence, the maximum of the parabola is half way between the roots, i.e. at x= 2.


It means that the maximum speed is (substitute x= 2 into the given formula)


     = 4*2 - 2^2 = 8 - 4 = 4 m/s.     ANSWER


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