A student is tracking the $\backslash ($ y $\backslash )-$axis motion of two balls $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash ),$ rotating in a horizontal plane. The two particles have concentric paths.

The graphs representing the $\backslash ($ y $\backslash )-$displacement versus time for the two balls are shown below. The solid line corresponds to ball $\backslash ($ A $\backslash ),$ while the dotted line corresponds to ball $\backslash ($ B $\backslash ).$

b$.$ How do the maximum speed of the balls compare? Choose the correct answer and justify your choice.

$($i$)$ ball $\backslash ($ A $\backslash )$ is moving faster than ball $\backslash ($ B $\backslash ).$

$($ii$)$ ball $\backslash ($ A $\backslash )$ has the same speed as ball $\backslash ($ B $\backslash ).$

$($iii$)$ ball $\backslash ($ A $\backslash )$ is moving slower than ball $\backslash ($ B $\backslash ).$

c$.$ How do the tangential accelerations of the balls compare? Choose the correct answer and justify your choice.

$($i$)$ the tangential acceleration of ball $\backslash ($ A $\backslash )$ is greater.

$($ii$)$ their tangential accelerations are equal.

$($iii$)$ the tangential acceleration of ball $\backslash ($ B $\backslash )$ is greater.

d$.$ Use the graph to calculate the normal acceleration of ball $\backslash ($ A $\backslash ).$