# Newtons work and double derivative.

1. Jul 19, 2011

### vkash

I have read kinematics and laws of motion(1st,second and third). In these two chapters one thing i found that
firstly distance is taken as first assumption.then it's derivative as velocity OK.
then it's(velocity) derivative is taken as acceleration OK.
Then it's derivative(acceleration) is not taken!!. but why he(our hero newton) stops at acceleration why not create another quantity named say X which is derivative of acceleration. Is he leave it for vikash(me) to do hahaha LOL!!!!(joke)
all derivative are with respect to time.
I have an answer for my own question.
(1) all motions can be defined on the basis of these three quantities.(mention am i correct here)

we all have felt force either due to gravity or due to lifts. when lift moves upward with due to changing velocity we feel extra force. How it feels of having changing acceleration? I mean if a lift is moving upwards with acceleration 2t (t is time). time varying acceleration. then how will it feel.

2. Jul 19, 2011

### DickL

The 3rd derivative of distance is called 'jerk' and it is often used in analysis of non-constant acceleration, such as in harmonic systems. If you think about the effect of a change in acceleration, as when standing in a bus and starts up, you are jerked, hence the name.

When considering acceleration due to gravity, the acceleration is constant and therefore the 3rd derivative, jerk, is zero. All of the mechanics work by Newton, that I'm aware of, was dealing with gravity as the acceleration force, or another constant value force, thus no need for the 3rd derivative.

3. Jul 19, 2011

### chrisbaird

The fact that your book does not take a derivative of acceleration with respect to time just means that your book is over-simplified. The third derivative of position with respect to time (or the derivative of acceleration with respect to time) is known as the "http://en.wikipedia.org/wiki/Jerk_%28physics%29" [Broken]" and is very important. If you think about it, F = ma tells us that whenever a force changes in time, then the acceleration changes in time and there is a jerk. Examples of the force changing in time would be: pressing the gas pedal of a car from half-way down to all the way down, having a cord break while Bungee jumping, accelerating down a hill on a bicycle and hitting a rock, etc. It is called a jerk because it feels like a jerk.

Last edited by a moderator: May 5, 2017
4. Jul 19, 2011

### chrisbaird

The acceleration due to gravity is only constant as a local approximation. The gravitational force (and thus the acceleration) depends on the separation of the two objects. Objects farther away from the earth experience less of its gravity and have a lower acceleration. But this spatial variation in gravitational force is so small for human-sized objects that the jerk can be ignored. For larger, farther objects such as comets, the change in acceleration becomes important.

5. Jul 19, 2011

### xts

Newton's equations fully describe the behaviour of (classical) cellestial mechanical system using position, velocity and acceleration with no need to use higher derivatives.

"why he(our hero newton) stops at acceleration why not create another quantity"
Bacause he (contrary to many people) obeyed Occam's principle: don't create non-necessary entities.