How Is Average Velocity Calculated in Multi-Stage Vector Displacements?

[Sullivan]

You go for a short walk traveling in three stages. The first displacement is 58.5 m 20.0 degrees east of north. The second displacement is 78.0 m 40.0 degrees south of east. Finally you go 99.0 m 17.0 degrees north of west. The answer I got was 36.9 m, 66.2 degrees north of west,which is correct.

But then they ask: If this trip took 125 seconds, what was the average velocity? They give the answer: 0.295 m/s, 66.2 degrees north of west.

What I got for that answer was 1.884 m/s. I figured you could just use the V avg = total displacement over time equation. So 58.5 + 78 + 40 / 125 = 1.844.

What am I doing wrong here?

Thanks for the help!

 

[Gauss]

Hey Sullivan.

Velocity is a vector function, so direction is important. Displacement refers to the distance between an initial and final point; in this case, your initial point is where you start and your final point is where you end. You found that the distance between these two points is 36.9 m. So, in the period of 125 seconds, you moved to a position 36.9 m from your initial position.

Velocity is found by dividing the displacement by time. so you have to divide 36.9/125 = .2952 m/s.

Anything unclear?

 

[Sullivan]

Right! Thank you very much. I was using total distance rather than displacement wasn't I!

 

[Gauss]

Yep! You were calculating the speed as opposed to the velocity, these two are often confused as are distance and displacement.