Compare graphs a and b in figure 11-2 which graph shows a greater velocity at 5 seconds? at 10 seconds? that. describe how you know.

At 5 seconds, graph a shows a greater velocity. At 10 seconds, graph b shows a greater velocity.

Explanation:

In a distance-time graph, the slope of the curve corresponds to the velocity of the object. In fact, the slope of the curve is defined as:

where is the variation of the y-variable and the variation of the x-variable.

In a distance-time graph, the y variable is the distance, while the x-variable is the time. Therefore, the slope of the curve corresponds to the ratio between the variation in distance and the variation in time:

However, this is also the definition of velocity. Therefore:

- At 5 seconds, graph A has a greater slope, which means it shows a greater velocity than graph B

- AT 10 seconds, graph B has a greater slope, which means it shows a greater velocity than graph A

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