What IS acceleration (besides a confusing concept) and a Newton / Joule?

Question

Well, I've researched my textbooks and wikipedia.
I think I may know the general idea of what it is, but I want to be sure.
This is what I think....

-So I read that Acceleration is the rate of change, and a Newton is the force required to accelerate 1 kg of a substance by 1 meter per second squared (1 kg * m / s2).
So if I have my meaning of Acceleration correct, then if something had an acceleration of 5 Newtons, then for every second passed, 1 kg of that substance would speed up 5 meters per second more? So if it starts out at 10 m/s, then in 3 seconds it would be going at a speed of 25 m/s? Is that right?

And I know that a Joule is "the energy expended by a force of one newton moving an object one meter along the direction of the force." but can someone explain that to me more?
So...if a block of concrete that weighed 1 kg was sliding down a hill with a force of one newton (meaning it sped up 1 meter more per second?) then for every meter it slid, that would be 1 Joule?

Answer 1

Hmm...Acceleration (from here on "a") is the rate of change of velocity (from here on "v"). So in other words, how many meters per second an object goes faster per second. The unit of a becomes then: meters/second² ("m/s²"). So in your problem you would have an "a" of 5"m/s²" and not 5Newton.
Newton is indeed the unit of force. And any force (you know the drill "F") is defined by the formula: F= mass ("m" m not being meters, but mass and thus in units of kg) *acceleration = "m"*"a".
Your first derivation is correct despite the incorrect use of units.

Joule is the unit of Work ("W"), work is defined as you said. This gives the formula (for a straight line that is) "W"="F"*"distance traveled". For an inclination (a hill of some sort) this becomes much more complicated, because the force acting on it isn't parallel to its distance travelled.
So lets say, you have a concrete block of 1kg which you pull forward with a force of 30 Newton along a path of 12 meters. The formula yields:
"W"=30Newton * 12metres = 360 Joules. So indeed, if you pull the same block with a force of 1 newton during 1 meter you get 1 Joule.


I hope this clarifies things a bit, just be carefull with those units, teachers can be picky on those :-)

Answer 2

Welcome Mr Shadow -

You are correct in your understanding of acceleration except when you said "an acceleration of 5 Newtons." I think you meant a acceleration of 5 m/sec^2.

As far as the energy part goes, the work or energy expended is equal to a force times a distance. In this case, pushing against a 1 kg mass with 1 Newton of force (resulting in 1 m/sec^2 acceleration) for a distance of 1 meter will accelerate the mass not to 1 meter / sec, but to a velocity that can be found using the relation:

v(2)^2 = v(1)^2 + 2ax where

v(2) = final velocity in meters / sec
v(1) = initial velocity in meters / sec
a = acceleration in meters / sec^2
x = distance in meters

What may be confusing you is that elapsed time is not a part of this equation.

If we start pushing with an initial velocity v(1) of 0, then after 1 meter at a force of 1 Newton (which results in 1 m/sec^2 acceleration when applied to a 1 kg mass), we will have a velocity v(2) of 1.414 meters / sec. This is the velocity resulting from expending 1 joule of work, or energy against a 1 kg mass.

This makes sense when you solve for the kinetic energy of the mass moving at that velocity. This can be found using:

E = (1/2) mv^2

With m = 1 kg, v= v(2) = 1.414 m/sec, we get that the kinetic energy = 1 joule at a velocity of 1.414 m/sec. This is how much work we did by pushing the mass for 1 meter, so energy is conserved.

Answer 3

Acceleration is the rate of change of velocity with respect to time, meaning that the velocity of a body under the influence of constant acceleration will increase by the same amount each second EVERY second: that`s why we give acceleration the units per sec^2, meaning "each second, every second"

You`re getting confused with the concept of acceleration and the power needed to produce a given acceleration in a body of given mass.