Expert: Daniel Mazur - 10/5/2005

Question
Im lost chathy
Hello,

This year I started home schooling for my last two years of school. And the Physical Science Is killing me!!!! Please can you help me find a formula for momentum\speed\acceleration velocity, and force? I'm clueless in finding the answer. How do I find the answers for questions like this:

An object travels 8 m in the 1st second of travel, 8 m again during the 2nd second of travel, and 8 m again during the 3rd second. It's accelerations in meters per second is:


Thanks!!!

Answer
Hi Jessica.

This is largely a matter of having the right book in your hands and/or the right teacher by your side. I strongly recommend to buy a book or a physics course. You didn't write, how old you are (...last two years of WHAT school I would like to ask). However, here you have a summary of the equations you asked for.

Momentum = Mass * Velocity
Force = Mass * Acceleration = Change of Momentum per unit time
Acceleration = Change of Velocity per unit time
Velocity = Change of Position per unit time

For practical calculations, you'll use the following eq.'s too. Let's assume an accelerated motion with a constant acceleration. Then the position r(t) dependence on time is

  r(t) = r_0 + v_0*t + (1/2)*a*t^2

(note: x_0 reads "ex-sub-zero" or "ex-naught" and x^2 reads "ex-squared"), where r_0 is the position of the object at t=0 and v_0 is the velocity of the object at t=0.

Simple observations of this single equation will tell you that:
* all variables are allowed to have positive, negative or zero values
* at t=0, the only (generally) non-zero term is r_0, so r(0)=r_0
* if you can choose to set the initial position freely, it's usually good to set it so that r_0=0 too
* if initial velocity is zero, it zeroes the second term, independent of time
* we classify motion of an object thus:
 a=0 -> motion at a constant velocity (if also v_0=0 then it is simply "standing still" motion) and the third term is zero independent of time
 a>0 -> accelerated motion
 a<0 -> decelerated motion

The second equation you will want to consider is the time dependence of velocity

  v(t) = v_0 + a*t

If acceleration a=0, then you have just a constant-velocity motion v(t) = v_0.

I do not have capacity here to substitute three chapters of physics 101, so I'll move on to your problem:

Quote:"An object travels 8 m in the 1st second of travel, 8 m again during the 2nd second of travel, and 8 m again during the 3rd second. It's accelerations in meters per second is:"

Solution:

What information have I been given?
The info given is, in other words, that for three consecutive time periods of 1 second the travelled distance was ALWAYS THE SAME. The fact that this distance was 8 meters will translate into "average speed was 8 m/s for each of the three periods", but the value itself doesn't matter for the solution, as you'll see later.

What did they ask for?
Acceleration.

How to approach it?
Q: What is Acceleration?
A: Change of Velocity in time.
Q: Did the velocity change in time?
A: NO!!! I has been 8 m/s in ALL three measurements.
Q: How does "NO" translate into numbers?
A: "NO" acceleration (nor deceleration) means 0 (i.e. ZERO) m/s^2

If you look carefully, the problem as you wrote it down had a mistake in its formulation already. The physical dimensions of an acceleration are m/s^2 (read "meters-per-second-squared"), not "meters per second". You have to be very punctual in these things in order to make a good science student.

Please do read a few chapters of a textbook and you will get to see through it gradually. I'd recommend Physics from Halliday, Resnick and Walker, which is used in the first college years, but is written in a very accessible way even for students much younger.

Don't hesitate to ask me some more, if you need, I'll be happy to help.

Good luck!
Daniel