- #1
madah12
- 326
- 1
Homework Statement
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 what's causing them motion?
I am talking about only at t=0
i know the velocity isn't 0 other where but i am saying
at t=0the velocity is 0 and it should have 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 don't give me the same unsatisfactory reply :X
Homework Equations
v=dx/dt
a=dv/dt