A jogger runs in a straight line with an average velocity of v1=6.6 m/s for t1=6.0 min, and then with an average velocity of v2=5 m/s for t2=3.0 min. What is her average velocity during this time? Answer in units of m/s.
distance1=velocity1*time1
distance2=velocity2*time2
avgvelocity=(distance1+distance2)/totaltime
To find the average velocity, we can use the formula:
Average Velocity = Total displacement / Total time
The total time can be calculated by adding the individual times:
Total time = t1 + t2
Total time = 6.0 min + 3.0 min = 9.0 min
Since we need the answer in m/s, we need to convert the total time from minutes to seconds since velocity is measured in meters per second. There are 60 seconds in a minute, so:
Total time = 9.0 min * 60 sec/min = 540 sec
The total displacement is the sum of the individual displacements. We can calculate the displacements using the formula:
Displacement = Average velocity * Time
For the first part of the jog, the displacement is:
Displacement1 = v1 * t1
Displacement1 = 6.6 m/s * 6.0 min = 39.6 m
For the second part of the jog, the displacement is:
Displacement2 = v2 * t2
Displacement2 = 5 m/s * 3.0 min = 15 m
The total displacement is the sum of the individual displacements:
Total displacement = Displacement1 + Displacement2
Total displacement = 39.6 m + 15 m = 54.6 m
Now we can calculate the average velocity:
Average velocity = Total displacement / Total time
Average velocity = 54.6 m / 540 sec
Average velocity = 0.1 m/s
Therefore, the jogger's average velocity during this time is 0.1 m/s.