22 Jan '10 03:456 edits

hello all, stuck on a problem looking for some insight

A particle travels along the path, y^2 = 4x with a constant speed of V = 4(m/s). determine the x, and y components of the particles velocity and acceleration when the particle is at x = 4(m)

im going to use prime notation for ease of formatting

heres where im at so far

a particles velocity is tangent to its path so I need to find the slope of the function at the given x

y^2 = 4x

2y*y'(x) = 4

y'(x) = 2/(y)

y'(4) = 1/2

from here I can find Vx,and Vy (the x-y components of the velocity respectivley)

from the right triangle (2,1,Sqrt(5))

@x=4......{y'(t) =Vy = ||V||*1/sqrt(5) = 4/sqrt(5)

..............{x'(t) = Vx = ||V||*2/sqrt(5) = 8/sqrt(5)

Now to find the components of the acceleration

y'(x) = 2/y

y'(t) = (2/y)(x'(t))

y"(t) = 2*[(-1/y^2)*(y'(t))*(x'(t)) + (1/y)(x"(t))]

here is where im stuck

1 equation 2 unknows and i'm having trouble coming up with another independent equation for either

y"(t) or x"(t)

does anyone see something about the acceleration that could help me out?

A particle travels along the path, y^2 = 4x with a constant speed of V = 4(m/s). determine the x, and y components of the particles velocity and acceleration when the particle is at x = 4(m)

im going to use prime notation for ease of formatting

heres where im at so far

a particles velocity is tangent to its path so I need to find the slope of the function at the given x

y^2 = 4x

2y*y'(x) = 4

y'(x) = 2/(y)

y'(4) = 1/2

from here I can find Vx,and Vy (the x-y components of the velocity respectivley)

from the right triangle (2,1,Sqrt(5))

@x=4......{y'(t) =Vy = ||V||*1/sqrt(5) = 4/sqrt(5)

..............{x'(t) = Vx = ||V||*2/sqrt(5) = 8/sqrt(5)

Now to find the components of the acceleration

y'(x) = 2/y

y'(t) = (2/y)(x'(t))

y"(t) = 2*[(-1/y^2)*(y'(t))*(x'(t)) + (1/y)(x"(t))]

here is where im stuck

1 equation 2 unknows and i'm having trouble coming up with another independent equation for either

y"(t) or x"(t)

does anyone see something about the acceleration that could help me out?