If a runner travels at a speed of 10 m/s for 5 seconds, stops for a short time then continues on at a speed of 8 m/s for 4 seconds. How long was the runner stopped for if his average speed at the end of the trip is 4 m/s.
To solve this problem, we can use the formula for average speed:
Average speed = total distance / total time
First, let's find the total distance the runner covered. We know the runner traveled at a speed of 10 m/s for 5 seconds, so the distance covered during that time is:
Distance = speed × time
Distance = 10 m/s × 5 s
Distance = 50 m
Next, the runner stopped for a short time and then continued at a speed of 8 m/s for 4 seconds. So, the distance covered during that time is:
Distance = speed × time
Distance = 8 m/s × 4 s
Distance = 32 m
Now let's combine the distances to get the total distance:
Total distance = 50 m + 32 m
Total distance = 82 m
We also know the average speed at the end of the trip is 4 m/s. To find the total time, we'll rearrange the formula for average speed:
Total time = total distance / average speed
Total time = 82 m / 4 m/s
Total time = 20.5 s
Now, we can calculate the time the runner was stopped for:
Stopped time = total time - (5 s + 4 s)
Stopped time = 20.5 s - 9 s
Stopped time = 11.5 s
Therefore, the runner was stopped for 11.5 seconds.