(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let's say an object is moving with x(t)= e^(-1/t^2)

it's motion is continuous everywhere and differentiable because its exponential

so v(t)= 2e^(-1/t^2)/t^3

a(t)= e^(-1/t^2) *(4-6t^2)/t^6

I have asked to a calculus teacher and he said all the derivatives will be 0 at t=0

yet if all the derivatives are 0 then one would not expect the object to move in time but for any t>0 x(t) >0 but there is no velocity to move the object ,no acceleration to increase the velocity and no jerk to make acceleration etc

so whats causing them motion?

I am talking about only at t=0

i know the velocity isnt 0 other where but i am saying

at t=0the velocity is 0 and it shoulda stayed 0 so is acceleration etc because all the derivatives that may increase it is 0 i asked this before and got a reply y=x^4 has derivative 0 at t=0 but still increase though d^4(y)/dx^4 = 4 which is a positive number that increase d the third derivative to increase the second derivative to increase the first derivative to increase the function value so please dont give me the same unsatisfactory reply :X

2. Relevant equations

v=dx/dt

a=dv/dt

3. The attempt at a solution

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# Basic kinematics confusion all derivatives 0?

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