Question

the following graph represents the motions of two speedboats, green and blue, during a 100 m race. which boat accelerates faster off the starting line? the green boat the blue boat

Explanation:

Step1: Analyze the slope of the graph

In a position - time graph, the slope of the graph represents the velocity. For an accelerating object, the slope of the position - time graph is changing.

Step2: Compare the slopes of the two boats

The green boat has a constant slope (constant velocity as its graph is a straight line). The blue boat has a changing slope. At the start (near \(t = 0\)), the blue boat has a smaller slope (lower initial velocity). But as time progresses, the slope of the blue boat's graph becomes steeper. A steeper slope in a position - time graph means a higher velocity. Since acceleration is the rate of change of velocity, a changing slope (for the blue boat) implies acceleration, and a steeper slope (compared to its initial slope and the green boat's constant slope) means it is accelerating.

Answer:

The blue boat