Final answer:
The time for a to-and-fro swing on a playground swing remains unchanged when a child stands up because the period of swing depends only on the length of the pendulum and the acceleration due to gravity, not the position or mass of the child.
Step-by-step explanation:
If a child standing on a playground swing stands up, her time for a to-and-fro swing is unchanged. The time period of a simple pendulum, which a swing essentially is, is not dependent on the mass of the swinging object but on the length of the pendulum and the acceleration due to gravity. Specifically, the period T is given by T = 2πsqrt(l/g), where l is the length of the pendulum and g is the acceleration due to gravity. Standing up on the swing does not change the length of the ropes or the acceleration due to gravity, and hence the time for a to-and-fro swing remains the same.