A jogger runs eastward in a straight line with an average speed of 2 m/s for 5
minutes and then continues with an average speed of 1.5 m/s for 2 minutes.
a. What is the total distance he went?
b. What is his average velocity during this time?
To find the answers to these questions, we'll need to calculate the distance traveled during each interval and find the total distance. We'll also need to calculate the average velocity, which is different from the average speed because it includes direction.
a. To find the distance traveled during each interval, we'll use the formula:
Distance = Speed x Time
For the first interval, the speed is 2 m/s and the time is 5 minutes. Since the speed is in meters per second and the time is in minutes, we need to convert the time to seconds by multiplying by 60.
Distance_1 = 2 m/s x (5 minutes x 60 seconds/minute) = 600 meters
For the second interval, the speed is 1.5 m/s and the time is 2 minutes (converted to seconds).
Distance_2 = 1.5 m/s x (2 minutes x 60 seconds/minute) = 180 meters
The total distance is the sum of the distances traveled during each interval:
Total distance = Distance_1 + Distance_2 = 600 meters + 180 meters = 780 meters
Therefore, the jogger went a total distance of 780 meters.
b. Average velocity is calculated by dividing the total displacement by the total time. Displacement is the change in position, considering both distance and direction.
The jogger is running eastward during both intervals, so the displacement is:
Displacement = Distance_1 - Distance_2 = 600 meters - 180 meters = 420 meters
The total time is the sum of the times for both intervals:
Total time = 5 minutes + 2 minutes = 7 minutes = 7 x 60 seconds = 420 seconds
Average velocity = Displacement / Total time = 420 meters / 420 seconds = 1 meter/second
Therefore, the jogger's average velocity during this time is 1 meter/second, eastward.