Question

A football quarterback runs 15.0 m straight down the playing field in 2.50 s. He is then hit and pushed 3.00 m straight backward in 1.75 s. He breaks the tackle and runs straight forward another 21.0 m in 5.20 s. Calculate his average velocity (a) for each of the three intervals and (b) for the entire motion.

a) (a) 6.0 m/s, -1.71 m/s, 4.04 m/s, (b) 1.27 m/s
b) (a) 6.0 m/s, -1.71 m/s, 4.04 m/s, (b) 2.38 m/s
c) (a) 6.0 m/s, -1.71 m/s, 4.04 m/s, (b) 3.15 m/s
d) (a) 6.0 m/s, -1.71 m/s, 4.04 m/s, (b) 4.42 m/s

Answer 1

The average velocity for each interval is 6.0 m/s, -1.71 m/s, and 4.04 m/s. The average velocity for the entire motion is 3.49 m/s.

Step-by-step explanation:

The average velocity for each of the three intervals can be calculated by dividing the total displacement by the total time taken.

Interval 1: Down the playing field

1. Displacement = 15.0 m
2. Time = 2.50 s
3. Average velocity = Displacement / Time = 15.0 m / 2.50 s = 6.0 m/s

Interval 2: Pushed backward

1. Displacement = -3.00 m (negative because he moved backward)
2. Time = 1.75 s
3. Average velocity = Displacement / Time = -3.00 m / 1.75 s = -1.71 m/s

Interval 3: Run forward after breaking the tackle

1. Displacement = 21.0 m
2. Time = 5.20 s
3. Average velocity = Displacement / Time = 21.0 m / 5.20 s = 4.04 m/s

For the entire motion, the total displacement is 15.0 m - 3.00 m + 21.0 m = 33.0 m, and the total time is 2.50 s + 1.75 s + 5.20 s = 9.45 s.

Therefore, the average velocity for the entire motion is Average velocity = Total displacement / Total time = 33.0 m / 9.45 s = 3.49 m/s.

Answer 2

The quarterback's average velocity for each interval is 6.0 m/s, -1.71 m/s, and 4.04 m/s, respectively. The average velocity for the entire motion is 3.49 m/s, which is not listed among the provided options.

Step-by-step explanation:

To calculate the average velocity for each interval of the quarterback's motion, we divide the total displacement by the time interval for that segment.

For the first interval: Average velocity = 15.0 m / 2.50 s = 6.0 m/s

For the second interval, because he is pushed backward, the displacement is negative: Average velocity = -3.00 m / 1.75 s = -1.71 m/s

For the third interval: Average velocity = 21.0 m / 5.20 s = 4.04 m/s

To find the average velocity for the entire motion, we sum up the total displacement (which is positive when moving down the field and negative when pushed backward) and divide by the total time.

Total displacement = 15.0 m - 3.00 m + 21.0 m = 33.0 m

Total time = 2.50 s + 1.75 s + 5.20 s = 9.45 s

Average velocity for the entire motion = Total displacement / Total time = 33.0 m / 9.45 s = 3.49 m/s

That means the correct answer is not listed in the provided options.