How Do You Calculate Average Velocity for Multiple Directions?

[pinkxoxo]

Homework Statement

A train moving at a constant speed of 51.0 km/h moves east for 38.0 min, then in a direction 53.0° east of north for 16.0 min, and finally west for 64.0 min. What is the average velocity of the train during this run?

Magnitude? km/h

Direction?
° (counterclockwise from east)

Homework Equations

I don't even know what equations to use. I know average velocity is displacement/time but idk where to start from

The Attempt at a Solution

No attempts I am lost help please!

 

[gabbagabbahey]

Like you said, average velocity=displacement/time. So you need to start by calculating the total displacement and the total time elapsed.

 

[pinkxoxo]

ok the total time would be all the times added together but how do i find the total displacement

 

[pinkxoxo]

T=118 mins but i need to convert to hours so that's 1.967 hours

 

[HallsofIvy]

The displacement is the vector that goes straight from the initial point to the final point. You can find it from the information given by adding components or by trigonometry.

 

[gabbagabbahey]

The total displacement will be the vector sum of the three individual displacements (i.e. $\vec{d}_{tot}=\vec{d}_1+\vec{d}_2+\vec{d}_3$) So start by computing those:

If the train travels 51.0 km/hr due East for 38.0min, what is its displacement $\vec{d}_1$? (You may as well call East the positive x-direction and North the positive y-direction)

 

[pinkxoxo]

oooohhhh ok hold on so i calculated each of the displacements by dividing the v by the t given and added them all together and tried to divide by the total time in hours and i got 162.46 km/h but it says I am wrong

 

[gabbagabbahey]

That's because they don't all point in the same direction. They are vectors and need to be added like vectors, not scalars.

 

[pinkxoxo]

ok i still got it wrong! GOD AND I HAVE 30 mins left to do this
and i need to finish my other probs

 

[gabbagabbahey]

If you show me your work, I can tell you where you are going wrong (P.S. it's usually a bad idea to leave your physics assignments to the last minute ;0) )

 

[pinkxoxo]

welll...i had a busy weekend lol. But i have been workin since 8 in the morning! but i want to take the trig approach. but my work is this ok......(51/.633333)+(51/.267)+(51/1.067)<--but i made that neg bc it goes left? then i divided by all the times added together and converted to hours which was 1.967 hours

 

[gabbagabbahey]

For starters, displacement=velocity*time not velocity/time.

Secondly, you are adding them as if they are all in the same direction, but they're not...the first one points east, the second point 53 deg east of north and the 3rd one point west. draw a picture to help you see what is going on.

 

[pinkxoxo]

X_X NO WONDER and i drew the pic i just don't know wut to do with it..i was going to try to use trig but I am so freakin lost on this problem

 

[gabbagabbahey]

hmmm... start by computing each of the 3 distances (just the distance, not the displacement)

 

[pinkxoxo]

ok and i calculate by v=d/t so d=v/t which is wut i did earlier when i was dividing v by t and that's how i got my d's for example (51/.63333)

 

[gabbagabbahey]

v=d/t implies d =v*t not v/t

 

[pinkxoxo]

Thank u for all of your help but my thing is due and i requested an extension but i think I am just going to leave it at what i have and get an 88 thank u once again...I'm glad i got an account on this bc ppl are very helpful when it comes to my webassign problems

 

[pinkxoxo]

and oh yeah ur right idk wtf i was thinking! it is v*t..(STUPID MISTAKE) i promise I am not dumb just more of a calculus person as opposed to physics and i know that they r basically the same but there is a difference to me my mind just works differently maybe its bc calculus isn't polluted with words and laws of dimensions and stuff its just plain 'ol math and yeah nvm I am going off on a tangent XD

 

[pinkxoxo]

woah my other posts got deleted weird thanks for the help