A runner moving at a velocity of 6 m/s increases their velocity over a 2 s time interval to a rate of 10 m/s. What is the rate of acceleration?

To determine the rate of acceleration, we can use the formula for acceleration, which is defined as the change in velocity divided by the time over which that change occurs. In this scenario, the runner's initial velocity is 6 m/s, and their final velocity after 2 seconds is 10 m/s.

First, we calculate the change in velocity by subtracting the initial velocity from the final velocity:

Change in velocity = Final velocity - Initial velocity = 10 m/s - 6 m/s = 4 m/s.

Next, we take this change in velocity and divide it by the time interval during which the change occurred:

Acceleration = Change in velocity / Time = 4 m/s / 2 s = 2 m/s².

Thus, the rate of acceleration is 2 m/s². This means the correct answer reflects the positive increase in velocity over that time interval. It is essential to note that acceleration can be positive or negative based on whether the object is speeding up or slowing down. In this case, since the runner's speed increased, the acceleration is positive, confirming that the correct choice is indeed 2 m/s².