# Question on basic kinematics

1. Oct 19, 2007

### bourne

1. The problem statement, all variables and given/known data
consider a particle moving in a straight line and assume that its position is defined by the equation,
x= 6(t^2) - (t^3)

2. Relevant equations

v=dx/dt= 12t - (3t^2) and
a=dv/dt= 12-6t

3. The attempt at a solution

the question is at t=0, x=0 at the origin the velocity is zero while the acceleration is 12 units. How's it possible that a particle is having zero velocity while it is accelerating??? i agree mathematically, but wat about the physics?
suppose if i consider instantaneous velocity.
it's limit t tends to zero dx/dt.
dx=infinitesimally small distance= x(at position 2) - x(position 1)= x(2) - x(1)
x(1)=0, that is origin. if x(2) is very very close to x(1), then the limit t tends to zero dx/dt will become zero that is instantaneous velocity will become zero.
But in that very very small time 'dt', if particle did travel infinitesimally very small distance 'dx', such that the instantaneous velocity is zero, then how could there be acceleration in that same interval of time 'dt' ?

Last edited: Oct 20, 2007
2. Oct 20, 2007

### Gokul43201

Staff Emeritus
A ball is throw vertically up. What is its velocity at the top? What is its acceleration?

3. Oct 20, 2007

### learningphysics

Even though dx = 0 over some time dt... doesn't mean dv = 0 over that same time dt...

4. Oct 20, 2007

### bourne

if a particle didn't move the distance dx, how can it have velocity then?
m pretty confused. Is there any mathematical justification?
is thr any mechanics stuff that u want me to go through so that i can make myself clear?

5. Oct 21, 2007

### Gokul43201

Staff Emeritus
It can not, but it can have an acceleration. dv is related to acceleration, not velocity.
Yes. There is no reason that a function have zero slope at f(x)=0.

6. Oct 21, 2007

### bourne

this example is when we analyse things in the gravitational field.
Its a kind of conservative field. if a particle is placed anywhere near the surface of the earth it possess potential energy by virtue of its position.

Similar is the electromagnetic field.

But suppose we consider a fluid flow field like fluid flow in a pipeline or boundary layer flow over the aircraft, where the force due to gravity is cancelled by the boyant force of the fluid particle, fluid flows across two points due to the pressure difference, i come across the functions of position , velocity and accelerations, wherein after solving i find that particle velocity is zero while it has acceleration.

I dun't know whether u guys r geting me or not, anyways thanks for being patient and helping me out.

7. Oct 21, 2007

### learningphysics

Let's assume that 0 velocity => 0 acceleration. Suppose an object is at rest. Is motion possible for this object? Assume motion happens at some time t = 0. so for t<0 we have 0 velocity. But if motion happens at t = 0, then v>0 at t = 0... but that means there was an acceleration at some time t<0. but at t<0 we have 0 velocity and hence 0 acceleration according to our initial assumption...

contradiction. so no motion from rest is impossible.

0 velocity => 0 acceleration leads to the conclusion that motion from rest is impossible.

8. Oct 21, 2007

### bourne

okay i get ya