Question

Maria runs due east in a straight line with an average speed of 1.25 m/s for 5.01 min. Then she continues in the same straight-line

direction with an average speed of 1.06 m/s for 4.45 min.

a. Calculate Maria's total displacement.

b. Calculate Maria's average velocity during this entire jog?

Answer 1

Step-by-step explanation:

a. To calculate Maria's total displacement, we need to find the net distance and direction she has traveled. Since she has traveled in a straight line, we can simply add her two displacements together:

Displacement in first leg = (1.25 m/s)(5.01 min) = 375.625 m due east

Displacement in second leg = (1.06 m/s)(4.45 min) = 4.7117 m due east

Total displacement = 375.625 m + 4.7117 m = 380.3367 m due east

Therefore, Maria's total displacement is 380.3367 m due east.

b. To calculate Maria's average velocity, we need to find the total displacement and divide it by the total time. The total time is the sum of the time for each leg:

Total time = 5.01 min + 4.45 min = 9.46 min

Converting this to seconds: Total time = 9.46 min x 60 s/min = 567.6 s

Average velocity = Total displacement / Total time

Average velocity = 380.3367 m / 567.6 s

Average velocity = 0.67 m/s due east

Therefore, Maria's average velocity during this entire jog is 0.67 m/s due east.

Answer 2

a. Maria's total displacement is approximately **657.17 meters**.

b. Maria's average velocity during the entire jog is approximately **1.16 m/s**.

Solving for Maria's Total Displacement and Average Velocity:

**a. Total Displacement:**

To find Maria's total displacement, we need to consider both distances she covered at different speeds. Since she runs in the same direction, we simply add the individual distances:

* **Distance during first segment:**

- Time (t1) = 5.01 min = 5.01 * 60 s = 300.6 s

- Speed (v1) = 1.25 m/s

- Distance (d1) = v1 * t1 = 1.25 m/s * 300.6 s = 375.75 m

* **Distance during second segment:**

- Time (t2) = 4.45 min = 4.45 * 60 s = 267 s

- Speed (v2) = 1.06 m/s

- Distance (d2) = v2 * t2 = 1.06 m/s * 267 s ≈ 281.42 m

* **Total Distance (d_total):**

- d_total = d1 + d2 = 375.75 m + 281.42 m ≈ 657.17 m

Therefore, Maria's total displacement is approximately **657.17 meters**.

**b. Average Velocity:**

Average velocity is the total displacement divided by the total time taken:

* **Total Time (t_total):**

- t_total = t1 + t2 = 300.6 s + 267 s = 567.6 s

* **Average Velocity (v_avg):**

- v_avg = d_total / t_total = 657.17 m / 567.6 s ≈ 1.16 m/s

Therefore, Maria's average velocity during the entire jog is approximately **1.16 m/s**.