consider a particle moving in a straight line and assume that its position is defined by the equation,
x= 6(t^2) - (t^3)
v=dx/dt= 12t - (3t^2) and
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' ?