For a twice-differentiable position vector r(t)=⟨x(t),y(t)⟩, a student writes in their notes:
"Speed =[x′′(t)]2+[y′′(t)]2."
Which of the following statements best evaluates the student’s claim?
a) The claim is correct because speed is the magnitude of acceleration.
b) The claim is incorrect; speed equals x′(t)+y′(t), the sum of the component velocities.
c) The claim is incorrect; speed is the magnitude of velocity and should be [x′(t)]2+[y′(t)]2.
d) The claim is correct only when the particle moves along a straight line.