Calculus Trajectory Problem (comment below)

Question

anonymous · Answer

r(t) = <3cost,5sint,4cost> for 0 ≤ t ≤ T suppose the circular path of this function is to be traversed at a constant speed of 15m/s. Find the description of the trajectory. On what interval of 0 ≤ t ≤ T is the circle traversed once?

Before this question the previous question was the same but find the speed using $$S(t) = u'(t)\sqrt{f'(u(t))^2+g'(u(t))^{2}+h'(u(t))}$$
u(t) = 1
u'(t) = dt in this case

I solved that and found that the speed came out to be 5.
Now I don't know how to solve for the time interval

anonymous · Answer

In the previous problem time was defined between $$0 \le t \le 2π$$

anonymous · Answer

Also made a mistake above..
u(t) = t
u'(t) = 1

anonymous · Answer

@Charollete r(t) is an ellipsoid?

anonymous · Answer

I believe so

anonymous · Answer

@sarahusher @FutureMathProfessor 

Can you guys help?

anonymous · Answer

@primeralph any idea?

primeralph · Answer

Still need help?

anonymous · Answer

Yea

anonymous · Answer

Any idea how I can find the time interval with constant speed of 15ms?

primeralph · Answer

Equate S to 15.

primeralph · Answer

All you have to do is find the time at which r(t+T) = r(t) = r(0).

primeralph · Answer

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