derivatives (I don't know what I did wrong)?

Question

I know derivatives backwards and forwards. But I keep missing whatever mistake I'm making here. The problem is 
A particle follows a path described by the position vector

(–3.0t, 5.0t + t^(3/5), 6.0 + t^2 – 2.0t^(3/4)) m, for t > 0.

What is its acceleration at t = 3.0 seconds? State your answer using unit vector notation.

I know that I have to take the derivative twice for each part of the position vector. I got the first and last one right, but keep missing the middle one for some reason.

so 5.0*t + t^(3/5)
first derivative 5 + 3/5*t^(-2/5)
second derivative 0 - 6/25*t^(-7/5)
substitute t=3
I keep getting -0.052 but the program says that's wrong.

What am I missing?

Anonymous · Accepted Answer

Differentiate the entire vector:

dv/dx = (-3.0, 5.0 + (3/5)t^(-2/5), 2t- (3/2)t^(-1/4) )

d2v/dx2 = (0, (-6/25)t^(-7/5), 2 + (3/8)t^(-5/4) )

Now substitute t = 3:

Ax = 0
Ay = -0.052   ... What you got
Az = 2.095

Now use the magnitude of vector equation [sqrt ((Ax)^2 + (Ay)^2 + (Az)^2)] to get the magnitude:
2.095.

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derivatives (I don't know what I did wrong)?

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