Constant velocity questions (average speed vs. average velocity)

cherryrocket

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 travelled 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?

Kurdt

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.

notnimdab2009

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