During a family road trip, you drive 200 km north in three hours. Afterwards, you drive 200 km south in two hours. Find the average speed and average velocity for your entire trip.
Average speed = 80 km/h, Average velocity = 0 km/h
Explanation
To find the average speed, we divide the total distance travelled by the total time interval. Since distance is a scalar quantity, we add both legs of the trip. To find the average velocity, we divide the total displacement by the total time interval. Displacement is a vector quantity; driving 200 km north and then 200 km south brings the driver back to the starting point, resulting in zero net displacement.
Solution Steps
Step 1: Calculate total distance travelled = 200 km + 200 km = 400 km
Step 2: Calculate total time interval = 3 h + 2 h = 5 h
Step 3: Calculate average speed = total distance travelled / time interval = 400 km / 5 h = 80 km/h
Step 4: Calculate displacement = 200 km (North) + 200 km (South) = 0 km
Step 5: Calculate average velocity = displacement / time interval = 0 km / 5 h = 0 km/h