A jogger runs in a straight line with an average velocity of 7.7 m/s for 4.5 minutes, and then with an average velocity of 2.8 m/s for 2.8 minutes. What is her total displacement? Answer in units of m.
To find the total displacement, we need to calculate the individual displacements for each segment and then sum them up.
Step 1: Convert the time intervals to seconds.
- The first segment is 4.5 minutes, which is equal to 4.5 * 60 = 270 seconds.
- The second segment is 2.8 minutes, which is equal to 2.8 * 60 = 168 seconds.
Step 2: Calculate the displacement for each segment using the formula:
Displacement = Velocity × Time
- For the first segment: Displacement1 = 7.7 m/s × 270 s = 2079 m
- For the second segment: Displacement2 = 2.8 m/s × 168 s = 470.4 m
Step 3: Calculate the total displacement by summing up the individual displacements:
Total displacement = Displacement1 + Displacement2 = 2079 m + 470.4 m = 2549.4 m
Therefore, the total displacement of the jogger is 2549.4 m.
To find the total displacement, we need to calculate the displacement for each part of the jog, and then sum them up.
The formula to calculate displacement is:
Displacement = Velocity x Time
For the first part of the jog, the average velocity is 7.7 m/s, and the time is 4.5 minutes. To find the displacement for this part, we convert minutes to seconds by multiplying 4.5 minutes by 60 seconds/minute:
Time = 4.5 minutes * 60 seconds/minute = 270 seconds
Displacement1 = 7.7 m/s * 270 seconds = 2079 meters
For the second part of the jog, the average velocity is 2.8 m/s, and the time is 2.8 minutes. Again, we convert minutes to seconds:
Time = 2.8 minutes * 60 seconds/minute = 168 seconds
Displacement2 = 2.8 m/s * 168 seconds = 470.4 meters
Now, to find the total displacement, we simply add the two displacements together:
Total Displacement = Displacement1 + Displacement2 = 2079 meters + 470.4 meters = 2550.4 meters
Therefore, the jogger's total displacement is 2550.4 meters.
total distance: 7.7*4.5*60 + 2.8*2.8*60 = 2549.4 m
total time: (4.5+2.8)*60 = 438 s
so, avg velocity is 2549.4/438 = 5.8 m/s