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.

Algebra ->  Graphs -> 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.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

v=4x-x%5E2
v=x%284-x%29
max at v=0
0=x%284-x%29
=>x=0->disregard
0=%284-x%29=>x=4
answer is 4m%2Fs

Answer by ikleyn(52780) About Me  (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)


    V%5Bmax%5D = 4*2 - 2^2 = 8 - 4 = 4 m/s.     ANSWER