Question

olivia is on a swing at the playground. if the swing is moving from w to z, at which point is her kinetic energy increasing and her potential energy decreasing? (based on a starting point of w) o w o x o y o z

Explanation:

• Potential energy is related to height (\(PE = mgh\), where \(m\) is mass, \(g\) is acceleration due to gravity, and \(h\) is height). As height decreases, potential energy decreases.
• Kinetic energy is related to speed (\(KE=\frac{1}{2}mv^{2}\), where \(m\) is mass and \(v\) is speed). As speed increases, kinetic energy increases.
• At point \(W\), the swing is at rest (speed \(v = 0\), so \(KE = 0\)) and at a relatively high height (so \(PE\) is high).
• As the swing moves from \(W\) to \(X\), the height of Olivia (on the swing) is decreasing (so \(PE\) is decreasing) and her speed is increasing (so \(KE\) is increasing).
• At point \(Y\), the swing has maximum speed (so \(KE\) is maximum) and minimum height (so \(PE\) is minimum), but the question asks for the region where \(KE\) is increasing and \(PE\) is decreasing. After \(X\) (towards \(Y\)), \(KE\) is still increasing (but we are looking for the segment of motion where the trend of \(KE\) increasing and \(PE\) decreasing is maintained as per the starting - point \(W\)).
• At point \(Z\), the swing is again at a relatively high - height (similar to \(W\)) and speed starts to decrease (opposite of the motion from \(W\) to \(X\)).

Answer:

X.