Q6: A car is decelerating as it approaches a red light. The table shows the car's velocity v at time t. Calculate the average rate of change over the interval from 5 to 10 seconds.
The rate of change is -4 meters per second per second.
To calculate the average rate of change of velocity over the interval from 5 to 10 seconds, we need to determine the change in velocity and divide it by the change in time.
Given the information in the question, we know that the car's velocity is changing at a rate of -4 meters per second per second, which is equivalent to -4 m/s^2. This means that the car is decelerating at a constant rate.
First, we can find the change in velocity by subtracting the initial velocity from the final velocity. Since the question only provides the rate of change and not the actual velocities, we cannot find the exact values. However, we can still calculate the rate of change based on the given information.
The rate of change (-4 m/s^2) represents how much the velocity decreases every second. Therefore, within the interval from 5 to 10 seconds, the change in time is 10 - 5 = 5 seconds.
Next, we can calculate the change in velocity. Since the rate of change is constant, we can multiply the rate (-4 m/s^2) by the change in time (5 seconds):
Change in velocity = Rate of change * Change in time
Change in velocity = -4 m/s^2 * 5 seconds
Change in velocity = -20 m/s
Now that we've found the change in velocity, we can calculate the average rate of change by dividing the change in velocity by the change in time:
Average rate of change = Change in velocity / Change in time
Average rate of change = -20 m/s / 5 seconds
Average rate of change = -4 m/s
Therefore, the average rate of change over the interval from 5 to 10 seconds is -4 meters per second.