A jogger runs eastward in a straight line with an average speed of 2.25 m/s for 4.98 min and then continues with an average speed of 1.58 m/s for 2.18 min. (Hint: time is in minutes and velocity is in meters/second)

(a) What is her total displacement (in m)?

_____________m

(b) What is her average velocity (in m/s) during this entire jog?

______________m/s

a) [(2.25 m/s * 4.98 min) + (1.58 m/s * 2.18 min)] * 60 s/min

b) (answer from a) / (4.98 min + 2.18 min) / (60 s/min)

To find the total displacement, we need to calculate the displacements for each segment of the jog and then sum them up.

First, let's find the displacement for the first segment when the jogger runs eastward with a speed of 2.25 m/s for 4.98 min:

Displacement = Velocity * Time

Displacement = 2.25 m/s * (4.98 min * 60 s/min) [Converting minutes to seconds]

Displacement = 2.25 m/s * 298.8 s

Displacement = 671.55 m [Round to two decimal places]

Next, let's find the displacement for the second segment when the jogger continues with a speed of 1.58 m/s for 2.18 min:

Displacement = Velocity * Time

Displacement = 1.58 m/s * (2.18 min * 60 s/min) [Converting minutes to seconds]

Displacement = 1.58 m/s * 130.8 s

Displacement = 206.34 m [Round to two decimal places]

Now, let's find the total displacement:

Total Displacement = Displacement of first segment + Displacement of second segment

Total Displacement = 671.55 m + 206.34 m

Total Displacement = 877.89 m [Round to two decimal places]

Therefore, the total displacement is 877.89 m.

To find the average velocity, we'll divide the total displacement by the total time:

Total Time = Time of first segment + Time of second segment

Total Time = 4.98 min + 2.18 min

Total Time = 7.16 min [Round to two decimal places]

Average Velocity = Total Displacement / Total Time

Average Velocity = 877.89 m / (7.16 min * 60 s/min) [Converting minutes to seconds]

Average Velocity = 877.89 m / 429.6 s

Average Velocity = 2.04 m/s [Round to two decimal places]

Therefore, the average velocity during the entire jog is 2.04 m/s.

To find the answers to these questions, we need to use the concept of average velocity and displacement.

(a) Displacement is a vector quantity that represents the change in position of the jogger. It can be calculated by finding the difference between the initial and final positions. Since the jogger is running in a straight line, the displacement is equal to the distance travelled.

For the first part of the jog, the jogger runs eastward at a speed of 2.25 m/s for 4.98 minutes. To find the distance travelled during this period, we can multiply the speed by the time:

Distance 1 = Speed 1 × Time 1

Distance 1 = 2.25 m/s × 4.98 min

Next, for the second part of the jog, the jogger continues at a speed of 1.58 m/s for 2.18 minutes. Again, we can calculate the distance travelled:

Distance 2 = Speed 2 × Time 2

Distance 2 = 1.58 m/s × 2.18 min

To find the total displacement, we need to add the distances travelled during both parts:

Total Displacement = Distance 1 + Distance 2

You can now substitute the values into the equation and calculate the total displacement in meters.

(b) Average velocity is a vector quantity that represents the displacement per unit time. It is calculated by dividing the total displacement by the total time taken.

Average velocity = Total Displacement / Total Time

To find the total time, we need to add the times taken for each part of the jog:

Total Time = Time 1 + Time 2

After calculating the total time, you can substitute the values into the equation and find the average velocity in meters per second.

By following these steps, you will be able to find the answers to both parts (a) and (b) of the question.