A jogger maintains a speed of 2.5 m/s for 188 m until he encounters a stoplight, and he abruptly stops and waits 27 s for the light to change. He then resumes his exercise and maintains a speed of 3.6 m/s for the remaining 51 m to his home.

(a) What was his average velocity for this entire time interval?
m/s

(b) What were his maximum and minimum velocities, and how do they compare with this average?
vmax = m/s
vmin = m/s

figure the entire time (time=distance/rate).

then avg veloicty=total distance/totaltime

To find the average velocity, we can use the formula:

Average velocity = Total displacement / Total time

To find the total displacement, we need to calculate the distance the jogger traveled from his starting point to the stoplight and then from the stoplight to his home.

Distance from starting point to stoplight = 188 m
Distance from stoplight to home = 51 m

Total displacement = Distance from starting point to stoplight + Distance from stoplight to home

To find the total time, we add the time it took for the jogger to reach the stoplight, the time he spent waiting at the stoplight, and the time it took for him to get to his home.

Time to reach the stoplight = Distance from starting point to stoplight / Speed = 188 m / 2.5 m/s
Time spent waiting at the stoplight = 27 s
Time to get to the home = Distance from stoplight to home / Speed = 51 m / 3.6 m/s

Total time = Time to reach the stoplight + Time spent waiting at the stoplight + Time to get to the home

Now we can plug in the values and calculate:

Total displacement = 188 m + 51 m = 239 m
Time to reach the stoplight = 188 m / 2.5 m/s = 75.2 s
Time to get to the home = 51 m / 3.6 m/s = 14.17 s
Total time = 75.2 s + 27 s + 14.17 s = 116.37 s

Average velocity = 239 m / 116.37 s

Now you can calculate the average velocity by dividing the total displacement by the total time.

For part (b), we can find the maximum and minimum velocities.

The maximum velocity is the highest speed during the jog, which is 3.6 m/s.
The minimum velocity is when the jogger stops at the stoplight, so it is 0 m/s.

To summarize:

(a) The average velocity for the entire time interval is [calculate the value] m/s.
(b) The maximum velocity is 3.6 m/s, and the minimum velocity is 0 m/s.