Let s(u) be a smooth curve in ℝ³. Which one of the following statements is false?
A: If s(u) is a circle on a plane then its acceleration is always zero.
B: The normal acceleration and the velocity of s(u) are always perpendicular.
C: The velocity of s(u) is always tangent to the curve.
D: The acceleration of s(u) is always tangent to the curve if and only if the curve is a straight line.
I think B and C are true because derivatives of vector-valued functions compute tangent vectors (which is the velocity) to the curves they describe.
Any help with regards to the other two statements to motivate the third correct statement would be greatly appreciated.
Thank you for taking the time to read my question.
I think A is false as the direction vector of the velocity is always changing in a circle so there must be normal acceleration