1
A runner dashes from the starting line (x = 0) to a point 130 m away and then turns around and runs to a point 11 m away from the starting point in 21 seconds. To the nearest tenth of a m/s what is the average speed?
2
What is the runner's average velocity in the previous problem?
1. average speed
Total distance
= 130 + 130 - 11
= 249 m
Total time = 21 s.
Average speed
= total distance / total time
=?? m/s
2. average velocity
Total displacement
=130-(130-11)
= 11
Total time
= 21 s.
Average velocity = total displacement/total time
= ?? m/s
avg velocity=changedisplacement/time=11m/21s
avg speed=changedistance/time=(130+130-11)/21 m/s
1. Well, it seems like this runner is really going the distance! Let's calculate their average speed.
The total distance covered is 130 m + 11 m = 141 m.
The total time taken is 21 seconds.
To find the average speed, we divide the total distance by the total time:
Average speed = 141 m / 21 s = 6.7 m/s (rounded to the nearest tenth)
2. Now let's put on our fancy math shoes and calculate the average velocity.
Average velocity is the displacement divided by the total time. The displacement is the change in position.
The runner starts at x = 0 and ends up at x = 11 m.
So the displacement is 11 m - 0 m = 11 m.
Average velocity = Displacement / Total time
Average velocity = 11 m / 21 s
Average velocity = 0.5 m/s
So the runner's average velocity is 0.5 m/s. They sure had a "positive" experience!
To find the average speed, we need to calculate the total distance traveled and divide it by the total time taken.
1. Total distance traveled:
The runner dashes from the starting line to a point 130 m away and then turns around and runs to a point 11 m away from the starting point.
Therefore, the total distance traveled is 130 m + 11 m = 141 m.
2. Total time taken:
The runner took 21 seconds to run this distance.
Average speed = Total distance / Total time
Average speed = 141 m / 21 s
To the nearest tenth of a m/s, the average speed is:
Average speed = 6.7 m/s
Now, let's move on to the second question.
To find the average velocity, we need to calculate the total displacement and divide it by the total time taken.
1. Total displacement:
The runner starts at x = 0 and runs to a point 11 m away from the starting point. The displacement is simply the final position minus the initial position.
Therefore, the total displacement is 11 m - 0 m = 11 m.
2. Total time taken:
The runner took 21 seconds to cover this displacement.
Average velocity = Total displacement / Total time
Average velocity = 11 m / 21 s
The average velocity is:
Average velocity = 0.52 m/s (rounded to two decimal places)
To find the average speed, we need to divide the total distance traveled by the total time taken.
1. Average speed:
The total distance traveled by the runner is the sum of the distances of the two legs of the race. The runner runs 130 m away from the starting line and then returns to a point 11 m away from the starting point. Hence, the total distance is 130 m + 11 m = 141 m.
The total time taken to cover this distance is given as 21 seconds.
To calculate the average speed, we divide the total distance by the total time:
Average speed = Total distance / Total time
Average speed = 141 m / 21 s
Calculating this gives us 6.7 m/s (to the nearest tenth).
2. Average velocity:
Velocity includes both speed and direction. When finding average velocity, we consider the displacement (change in position) and the total time taken.
Since the starting point is x = 0 and the runner eventually returns to x = 11 m, the displacement is +11 m.
The average velocity is given by:
Average velocity = Displacement / Total time
Average velocity = 11 m / 21 s
Calculating this gives us 0.5 m/s (to the nearest tenth).