need help for 1 SHM! (1 Viewer)

[Mainoyi]

A particle moves along the x-axis. It starts from rest at the point x = 1. Its acceleration is given by: acceleration = −4(x + 1/(x^3). Find its velocity when it is half-way from its starting point to the origin.

 

[Timothy.Siu]

A particle moves along the x-axis. It starts from rest at the point x = 1. Its acceleration is given by: acceleration = −4(x + 1/(x^3). Find its velocity when it is half-way from its starting point to the origin.

a= = −4(x + 1/(x^3)

vdv/dx= = −4(x + 1/(x^3)
1/2 v^2 = -2x^2 +2/x^2 +C
when v=0, x=1
-2+2+C=0
C=0

then, 1/2 v^2 = -2x^2 +2/x^2
so when x=1/2
1/2 v^2=-1/2 +8
v^2=15
v=+-root15
might've made a mistake.

 

[Mainoyi]

a= = −4(x + 1/(x^3)

vdv/dx= = −4(x + 1/(x^3)
1/2 v^2 = -2x^2 +2/x^2 +C
when v=0, x=1
-2+2+C=0
C=0

then, 1/2 v^2 = -2x^2 +2/x^2
so when x=1/2
1/2 v^2=-1/2 +8
v^2=15
v=+-root15
might've made a mistake.

thanks heaps..
didn't notice that when x=1,v=0...

 

[blake_ed]

"v=+ - root15"
perhaps should be
v=-root15 as velocity is to the left, which is -ve