Constant velocity questions (average speed vs. average velocity)

In summary, this conversation covers how to calculate average speed, direction, and displacement when motion is in a line.
  • #1
cherryrocket
19
0
5. Q: "A boat crosses a 2.85 km lake in 28 min. Find it's average velocity".
A: We want the answer in m/s, so I have to convert km to m, and min to s, right? Now I know how to do that, but not in the calculative way. I know that there is 1000 m in one km, so I multiplied 85 by 1000 and got 85 000 m. I know there is 60 s in one minute, so I multiplied 28 by 60 and got 1680 s. Then I divided 85 000 m / 1680 s and got 50.60 m/s


6. "Johann walks north at 6.5 km/h for 32 min. He then runs south at 18.5 km/h for 3.0 min."

First of all, I should convert everything to m/s, shouldn't I? So 6.5 km/h = 1.81 m/s, 32 min = 1920 s. 18.5 km/h = 5.14m/s, and 3.0 min = 180 s.

a. Q: What is Johann's average speed?
A: Since speed is scalar, I don't have to worry about the direction. So speed=total distance/total time

I need to get the distance of the northern direction, so I go: d=vt = d= (1.81m/s)(1920s) = 3475.2m

Then I get the distance of the southern direction; d=vt = d= (5.1
4m/s)(180s) = 925.2 m

So the total distance traveled was 4400.4 m.

The total time was 2100 s.

So to get the total speed: = total distance/total time = 4400.4 m / 2100 s = 2.09733 m/s
= 2.10 m/s (significant digits)


b. Q: Find Johann's average velocity.
A: Velocity is a vector, so you have to take direction into account. So when he goes north, the value of the distance is positive, and when he goes north the value is negative. So for total distance traveled to find the velocity I have to add both distances together: 3475.2m + (-925.2 m) = 2550 m.
And then I divide that by the total time (since time can never be negative):
2550m/2100 s = 1.21 m/s
Is that correct?
 
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  • #2
cherryrocket said:
5. Q: "A boat crosses a 2.85 km lake in 28 min. Find it's average velocity".
A: We want the answer in m/s, so I have to convert km to m, and min to s, right? Now I know how to do that, but not in the calculative way. I know that there is 1000 m in one km, so I multiplied 85 by 1000 and got 85 000 m. I know there is 60 s in one minute, so I multiplied 28 by 60 and got 1680 s. Then I divided 85 000 m / 1680 s and got 50.60 m/s

You should multiply 2.85 by 1000 to get 2.85km in meters.

6. "Johann walks north at 6.5 km/h for 32 min. He then runs south at 18.5 km/h for 3.0 min."

First of all, I should convert everything to m/s, shouldn't I? So 6.5 km/h = 1.81 m/s, 32 min = 1920 s. 18.5 km/h = 5.14m/s, and 3.0 min = 180 s.

a. Q: What is Johann's average speed?
A: Since speed is scalar, I don't have to worry about the direction. So speed=total distance/total time

I need to get the distance of the northern direction, so I go: d=vt = d= (1.81m/s)(1920s) = 3475.2m

Then I get the distance of the southern direction; d=vt = d= (5.1
4m/s)(180s) = 925.2 m

So the total distance traveled was 4400.4 m.

The total time was 2100 s.

So to get the total speed: = total distance/total time = 4400.4 m / 2100 s = 2.09733 m/s
= 2.10 m/s (significant digits)

That looks correct.

b. Q: Find Johann's average velocity.
A: Velocity is a vector, so you have to take direction into account. So when he goes north, the value of the distance is positive, and when he goes north the value is negative. So for total distance traveled to find the velocity I have to add both distances together: 3475.2m + (-925.2 m) = 2550 m.
And then I divide that by the total time (since time can never be negative):
2550m/2100 s = 1.21 m/s
Is that correct?

Remember velocity also has a direction. The method you have used in case you are wondering is finding the displacement and dividing it by the total time. That is how you calculate a general average velocity. In the special case where the motion is in a line you can add the two velocity vectors and divide by two.
 
  • #3
Kurdt said:
You should multiply 2.85 by 1000 to get 2.85km in meters.



That looks correct.



Remember velocity also has a direction. The method you have used in case you are wondering is finding the displacement and dividing it by the total time. That is how you calculate a general average velocity. In the special case where the motion is in a line you can add the two velocity vectors and divide by two.

Hi Kurdt ,

I am trying to search the forum for average velocity formula. In this problem example. What if the person in this example runs in straight line (north) instead of south. What is the correct computation for the average velocity? Is it (6.5 km/hr + 18.5 km/hr)/2 = 12.5 km/hr North or get the total displacement of walking and running then divide by the total travel time? If i do the latter, i am getting around 7.5 km/hr North. Can you pls confirm the correct method? Thanks
 

What is the difference between average speed and average velocity?

Average speed is the total distance traveled divided by the total time taken, while average velocity is the displacement divided by the total time taken. In other words, average speed is a scalar quantity and average velocity is a vector quantity that takes into account direction.

Can average velocity be zero even if the object is moving?

Yes, average velocity can be zero if the object is moving in a circular path or back and forth along the same path. This means that the displacement is zero, even though the object is still moving and changing its position.

What is the difference between instantaneous velocity and average velocity?

Instantaneous velocity is the velocity of an object at a specific point in time, while average velocity is the total displacement divided by the total time taken. Instantaneous velocity is a more precise measure of an object's velocity at a given moment, while average velocity gives a general idea of the object's overall movement.

Can average velocity be negative?

Yes, average velocity can be negative if the displacement is in the opposite direction of the chosen coordinate system. This means that the object is moving in the opposite direction of the positive direction of the coordinate system.

How can you calculate average velocity when the object is not moving at a constant velocity?

To calculate average velocity when the object is not moving at a constant velocity, you can divide the total displacement by the total time taken, or you can use the average velocity formula: average velocity = (final velocity + initial velocity) / 2. This takes into account the change in velocity over time.

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