Question

You drive a beatup pickup truck along a straight road for 8.4 km at 70 km/h, at which point the truck runs out of gasoline and stops. Over the next 30 min, you walk another 0 km farther along the road to a gasoline station.

(a) What is your overall displacement from the beginning of your drive to your arrival at the station ?
(b) What is the time interval it from the beginning of your drive to your arrival at the station ?
(c) What is your average velocity vavg from the beginning of your drive to your arrival at the station ? Find it both numerically and graphically.
(d) Suppose that to pump the gasoline, pay for it, and walk back to the truck takes you another 45 min. What is your average speed from the beginning of your drive to your return to the truck with the gasoline ?

Answer 1

The overall displacement is 8.4 km, the time interval is 0.62 hours, the average velocity is 13.55 km/h, and the average speed is 6.12 km/h.

Step-by-step explanation:

(a) To find the overall displacement, we need to calculate the difference between the initial position and the final position. The initial position is 0 km and the final position is 8.4 km + 0 km = 8.4 km. Therefore, the overall displacement is 8.4 km.

(b) The time interval can be calculated by adding the time it took to drive the 8.4 km (8.4 km / 70 km/h = 0.12 hours) and the time it took to walk the additional 0 km (30 minutes = 0.5 hours). Therefore, the time interval is 0.12 hours + 0.5 hours = 0.62 hours.

(c) Average velocity is defined as displacement divided by time interval. Therefore, the average velocity is 8.4 km / 0.62 hours = 13.55 km/h. Graphically, the average velocity can be represented by the slope of the displacement-time graph, which in this case is the line connecting the initial position (0 km) and the final position (8.4 km).

(d) Average speed is defined as total distance traveled divided by total time taken. The total distance traveled is 8.4 km + 0 km = 8.4 km, and the total time taken is 0.12 hours + 0.5 hours + 0.75 hours = 1.37 hours. Therefore, the average speed is 8.4 km / 1.37 hours = 6.12 km/h.