Question

Using the equation Xf = vt + x0, after completing a road trip, you have driven 500 miles. If you drove at an average velocity of 65 mph for 6.4 hours, what was your starting position (x0)?

A. 48 miles
B. 256 miles
C. 416 miles
D. 560 miles

Answer 1

Using the equation Xf = vt + x0 and substituting the given values, we should find the starting position for a 500-mile trip at an average speed of 65 mph for 6.4 hours. However, upon calculation, the result does not match the given answer choices, suggesting possible errors in the question or choices.

Step-by-step explanation:

The equation Xf = vt + x0 relates final position (Xf), velocity (v), time (t), and starting position (x0). Given that the final distance driven is 500 miles, the average velocity (v) is 65 mph, and the time (t) is 6.4 hours, we can rearrange the equation to solve for x0: x0 = Xf - vt. Plugging in the values we have: x0 = 500 miles - (65 mph × 6.4 hours). Calculating the product of 65 mph and 6.4 hours gives us 416 miles, which is the distance covered during the trip. Therefore, the starting position is 500 miles - 416 miles = 84 miles. However, this does not match any of the answer choices provided, indicating a potential error in the question or answer choices.