Understanding AVG Speed and AVG Velocity: Solving Skateboarder Problem

[Kadaj]

ok i got back my test today and its some basic stuff, but i don't get the difference between AVG speed and AVG velocity.

One of my problems was 'The length of the barrel of a blowgun is 1.2 meters. Upon leaving the barrel, a dart has a speed of 14 m/s. Assmuing that the dart was uniformly accelerated, how long does it take for the dart to travel the length of the barrel?' and for the answer I got .086s but the correct answer was .17 s

Can anyone explain to me how the teacher got this?

because all i did was 1.2/14 but to me it seems my teacher did 1.2/7 but why?

And for the second part 'A skate boarder accerates from rest to 26 m/s in 10 seconds. His avg speed over this time interval is ?.

The answer is 13 m/s but i have not a clue how he got this

Can someone explain to me?

Thanks in advance

 

[Doc Al]

One of my problems was 'The length of the barrel of a blowgun is 1.2 meters. Upon leaving the barrel, a dart has a speed of 14 m/s. Assmuing that the dart was uniformly accelerated, how long does it take for the dart to travel the length of the barrel?' and for the answer I got .086s but the correct answer was .17 s

Can anyone explain to me how the teacher got this?

because all i did was 1.2/14 but to me it seems my teacher did 1.2/7 but why?

You used the final speed of the dart as it left the barrel. But the speed while it's in the barrel goes from zero (it starts from rest) to the final speed of 14 m/s. For uniformly accelerated motion, the average speed is $v_{ave} = (v_i + v_f)/2$. So the average speed is only 7 m/s.

And for the second part 'A skate boarder accerates from rest to 26 m/s in 10 seconds. His avg speed over this time interval is ?.

The answer is 13 m/s but i have not a clue how he got this

Same idea.

 

[wais]

Hi there,

Understanding the difference between average speed and average velocity can be confusing, but let me try to explain it to you.

Average speed is the total distance traveled divided by the total time taken. In your first problem, the distance traveled was 1.2 meters and the speed was 14 m/s. So your calculation of 1.2/14 gives you the average speed, which is correct.

On the other hand, average velocity takes into account the direction of motion. It is the total displacement (change in position) divided by the total time taken. In this case, the dart starts at rest and ends at a speed of 14 m/s, so its displacement is 1.2 meters in the direction of motion. Therefore, the average velocity would be 1.2 meters/0.17 seconds, which gives you a value of 7 m/s. This is why your teacher did 1.2/7 instead of 1.2/14.

For the second part, the skateboarder accelerates from rest to 26 m/s in 10 seconds. This means that his final velocity is 26 m/s and his initial velocity is 0 m/s. Using the formula for average velocity, we get (26 m/s - 0 m/s)/10 seconds = 26/10 = 2.6 m/s. This is the average velocity, but the question asks for the average speed. Since the skateboarder is traveling at a constant acceleration, his average speed would be half of his final velocity, which is 13 m/s.

I hope this helps to clarify the difference between average speed and average velocity. Keep practicing and you'll get the hang of it!