Final answer:
The magnitude of the car's average acceleration is 5 m/s² when its velocity changes from 25 m/s to 50 m/s over 5 seconds, and the distance traveled during this period is 187.5 meters.
Step-by-step explanation:
The student has asked what the magnitude of the average acceleration of a car is when its velocity changes from 25 m/s to 50 m/s in the negative x direction over 5 seconds, as well as how far the car travels during this period.
To calculate the average acceleration, we use the formula a = (Vf - Vi) / t, where Vf is the final velocity, Vi is the initial velocity, and t is the time taken. Plugging in the values given: a = (-50 m/s - (-25 m/s)) / 5 s = (-50 m/s + 25 m/s) / 5 s = -25 m/s / 5 s = -5 m/s2. The negative sign indicates the direction of acceleration is in the negative x direction; however, the magnitude of acceleration is simply 5 m/s2.
To find the distance traveled, we can use the formula for average velocity Vavg = (Vi + Vf) / 2 and multiply by the time elapsed. So, the distance traveled is ((-25 m/s + (-50 m/s)) / 2) * 5 s = (-75 m/s / 2) * 5 s = -187.5 m. The negative sign indicates the direction of travel, but the magnitude is 187.5 meters.