Question

From time t = 0 to time t = 40 seconds, the areas under both curves are equal. Therefore, which of the following is true at time t = 40 seconds?

Option 1: The velocities of both curves are equal.
Option 2: The accelerations of both curves are equal.
Option 3: The distances traveled by both curves are equal.
Option 4: The slopes of both curves are equal.

Answer 1

The equal areas under both velocity-time curves from t=0 to t=40 seconds indicate that the distances traveled by the objects represented by the curves are equal.

Step-by-step explanation:

If the areas under both curves are equal from time t = 0 to time t = 40 seconds, it means that the distances traveled by both curves are equal. This is because the area under a velocity-time graph represents the displacement. Options 1 and 2 regarding velocities being equal or accelerations being equal are not necessarily true, as equal areas do not imply equal velocities or accelerations at a given time. Option 4, concerning the slopes being equal, also doesn't apply since the slope of the velocity-time graph is the acceleration, and equal areas under the curve do not mean equal slopes at a specific time.