A bus travels up a hill at a constant speed of 40 km/h and returns down the hill at a constant speed of 60 km/h. Calculate the average speed for the whole trip in m/s.
Question
A bus travels up a hill at a constant speed of 40 km/h and returns down the hill at a constant speed of 60 km/h. Calculate the average speed for the whole trip in m/s.
Solution
To calculate the average speed for the whole trip, we first need to understand that average speed is total distance divided by total time.
Step 1: Convert the speeds from km/h to m/s 1 km/h = 1000 m/3600 s So, 40 km/h = 40 * 1000 / 3600 = 11.11 m/s And, 60 km/h = 60 * 1000 / 3600 = 16.67 m/s
Step 2: Assume the distance of the hill (up or down) to be 'd' meters.
Step 3: Calculate the time taken to travel up and down the hill Time taken to travel up the hill = d / 11.11 Time taken to travel down the hill = d / 16.67
Step 4: Calculate total time taken Total time = Time up + Time down = d / 11.11 + d / 16.67
Step 5: Calculate total distance travelled Total distance = 2d (since the bus goes up and then down the hill)
Step 6: Calculate average speed Average speed = Total distance / Total time = 2d / (d / 11.11 + d / 16.67)
Solving this will give you the average speed for the whole trip in m/s.
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