Help with Physics: Motion in a Plane

[knitwit704]

I'm a homeschooler, using BJU Press's curriculum. It's normally great, but with my physics I'm struggling and can't seem to find any help. I'm in the kinematics section, dealing with motion in a plane and projectile motion and such, and I don't understand much of it. I need a lot of help with this. Please, if anyone could.

This would be a sample question (I think).

If a car is traveling south at a velocity of 110 km/hr, and after 2 minutes, is traveling west at a velocity of 110 km/hr, what was its acceleration throughout the curve?

Thank you for reading this.

 

[cepheid]

Welcome to PF knitwit704!

I'm a homeschooler, using BJU Press's curriculum. It's normally great, but with my physics I'm struggling and can't seem to find any help. I'm in the kinematics section, dealing with motion in a plane and projectile motion and such, and I don't understand much of it. I need a lot of help with this. Please, if anyone could.

This would be a sample question (I think).

If a car is traveling south at a velocity of 110 km/hr, and after 2 minutes, is traveling west at a velocity of 110 km/hr, what was its acceleration throughout the curve?

Thank you for reading this.

When being asked to compute physical quantities, it helps to know what the definitions of those quantities are. The mathematical definition of a quantity usually tells you exactly how to calculate it from other quantities. What is the definition of acceleration that you have been given?

Side note: please have a look at the PF site rules here:

https://www.physicsforums.com/showthread.php?t=414380

In particular:

Homework Help Guidelines

NOTE: You MUST show that you have attempted to answer your question in order to receive help. You MUST make use of the homework template, which automatically appears when a new topic is created in the homework help forums. Once your question or problem has been responded to, do not go back and delete (or edit) your original post.

Just be aware that in the future, questions such as these that don't make use of the template and don't have any attempt at a solution will be deleted.

 

[knitwit704]

Okay, I am sorry. I am new here. I will try to do that in the future.

 

[cepheid]

Okay...so, did you consider my question about acceleration? (That was the hint meant to help you with the problem).

 

[knitwit704]

Okay... acceleration is defined as:

acceleration is a noun that means:

Increase in the rate or speed of something.

The rate of change of velocity per unit of time

So obviously, as I already know, the unit would be whatever velocity unit you have over whatever unit of time (v/t), like m/s/s (I don't know how to do a squared symbol).

Also, can there be negative velocities? And negative accelerations? And what if both time units aren't the same, like the velocity is in km/hr and the time is in seconds? I know you need to convert one, but which one and how?

I'm sorry if this is bothersome.

 

[cepheid]

Okay... acceleration is defined as:

acceleration is a noun that means:

Increase in the rate or speed of something.

The rate of change of velocity per unit of time

I was hoping for a definition from your physics book, rather than a dictionary definition. In physics, physical quantities like acceleration have precise mathematical definitions. In this case, the part in boldface is correct. Acceleration is the change in velocity divided by the change in time: a = Δv/Δt, where the Greek letter delta (Δ) means "change in", in case you didn't know. So you have to do two things:

1. Compute the change in time during the motion. This is easy: no computation required, because it is given in the problem statement. The value of Δt is just the elapsed time of 2 minutes.

2. Compute the change in velocity. The change in a quantity is always the difference between the final value and the initial value. Δv = v_final - v_initial. But here's where it gets a bit tricky. The subtraction here is a subtraction of two vectors. Velocity is a vector: a quantity that has both a magnitude and a direction. The speed is the magnitude of the velocity. It is not different between the final state and the initial state. The speed is 110 km/h throughout. There is no change in speed. However, the direction is different between the final case and the initial case. Therefore there is a change in velocity. Have you worked with vectors before? Do you know how to subtract two vectors? You have to learn how to in order to solve this problem.

So obviously, as I already know, the unit would be whatever velocity unit you have over whatever unit of time (v/t), like m/s/s (I don't know how to do a squared symbol).

Writing (m/s)/s is fine. However, just for future reference, you can produce superscripts and subscripts using the tags [noparse] and [/noparse] respectively (put the text that you want to be superscripted or subscripted in between the tags. You can also click on the buttons marked X² and X₂ that appear above the box where you compose your replies, and these buttons will insert the tags for you.

Also, can there be negative velocities? And negative accelerations?

Yes, sort of. Like I said, velocity and acceleration are vectors, and vector have directions. If you had a one-dimensional problem (i.e. if your object was constrained to move along a 1D line), then there would be only two possible directions: "forward" and "back", and you could assign these + and - signs respectively. So a positive velocity would be in one direction, and a negative velocity would be in the opposite direction. However, this is a two-dimensional problem. The object can move anywhere in a 2D plane. So, instead of there being two possible directions, there are many. Typically you specify the direction using an angle, measured from some reference direction (e.g. North). So, you could have a velocity vector that points 30° East of North. Or 56.7° South of West. Or whatever. An alternative is to break up ("resolve") the vector into components that lie along two perpendicular axes (e.g. the North-South or vertical axis and the East-West or horizontal axis). Then your vector would turn into two vectors, one pointing along each direction. The components could either be positive or negative, depending on which direction along each axis that they pointed. I.e. the vertical component could be positive (Northward) or negative (Southward) and the horizontal component could be positive (Eastward) or negative (Westward). The overall vector would be the vector sum of the individual components. Here's an example of that, a vector resolved into two perpendicular components:

And what if both time units aren't the same, like the velocity is in km/hr and the time is in seconds? I know you need to convert one, but which one and how?

Typically in physics, we convert everything into the SI unit system which is short for "le Systeme International" (the International System of units). This system (a specific type of the metric system) is also known as the mks system, because the basic units of length, mass, and time in this system are the metre, the the kilogram, and the second. So you want to convert everything into these base units. Lengths should be in metres. Times should be in seconds.

Converting units is simple: it's like converting currencies. All you have to do is figure out how many of the first unit are contained in the second unit. For example how many seconds are there in an hour? Then you multiply (or divide) by this number, which is the conversion factor. E.g.

3 hours * (3600 seconds / 1 hour) = 10,800 seconds.

So I just converted 3 hours into seconds. Notice how the units work out: hours cancels on the top and the bottom, leaving you with seconds. Also notice how the conversion factor you multiply by (the thing in parentheses here) is always equal to 1, so you're not actually changing the value of the time interval, just the units it is expressed in.

How many metres are there in a KILO-metre? That should be obvious just from the prefix.

I'm sorry if this is bothersome.

It is a bit tedious and demanding. I will say this: an internet forum is suited to providing users with certain kinds of help. For example, Physics Forums is very suited to helping people apply the physics that they've learned to solving a particular problem, or to helping people better understand a specific concept. What you ask is not particular or specific. You seem to want to be taught introductory physics from scratch. An internet forum is not well-suited to this, and it is not a reasonable expectation on your part that people will take the time to do this for you. My recommendation is to keep reading. Your textbooks. Online lectures, like MIT OpenCourseWare. Even Wikipedia is perfectly suitable for providing such a basic level of physics knowledge. There is are also other sites, like hyperphysics:

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

Physics Forums has a post with some introductory physics equations:

https://www.physicsforums.com/showthread.php?t=110015

and a library that provides a glossary of terms with explanations and definitions:

https://www.physicsforums.com/library.php

 

[knitwit704]

Thank you. Once I have an actual problem that I need help with, I will come back here. Thank you for your time. And this was a particular concept, it was the concept of one of my chapters that I was struggling with.

Thank you again.