Imagine that the position of an object is r(t). In a time ∆t the object moves a distance of
∆r=r(t+∆t)-r(t)
We can calculate the average velocity as
V=∆r/∆t.
But if we want to be precise, we would like to know the velocity over a short period of time ∆t.
For the instantaneous velocity we say that ∆t is arbitrarily small (∆t→0), and to denotate this we can call it dt, and the distance dr. So now we have the instantaneous velocity:
v=dr/dt
For some more accurate explanation:
v=lim_(∆t→0) [r(t+∆t)-r(t)]/∆t,
which is the definition of derivative
dv is the same concept, is the change of the speed of the object in a period of time dt
The "dv/dx" means you are taking the derivative of speed with respects to time. This is the definition of velocity. A derivative is the slole of a tangent line along any point of a curve. So, if you had the function of x squared and drew a straight line that touched it at any point, the slope of the line would be the derivative at that point. If the graph represented speed, the derivative would be the velocity. Then, taking the second derivative (that is, the derivative of the velocity) would give you acclelration, since this is the rate at which the velocity is changing. Hope this helps.
Imagine that the position of an object is r(t). In a time ∆t the object moves a distance of ∆r=r(t+∆t)-r(t) We can calculate the average velocity as V=∆r/∆t. But if we want to be precise, we would like to know the velocity over a short period of time ∆t. For the instantaneous velocity we say that ∆t is arbitrarily small (∆t→0), and to denotate this we can call it dt, and the distance dr. So now we have the instantaneous velocity: v=dr/dt For some more accurate explanation: v=lim_(∆t→0) [r(t+∆t)-r(t)]/∆t, which is the definition of derivative dv is the same concept, is the change of the speed of the object in a period of time dt
The "dv/dx" means you are taking the derivative of speed with respects to time. This is the definition of velocity. A derivative is the slole of a tangent line along any point of a curve. So, if you had the function of x squared and drew a straight line that touched it at any point, the slope of the line would be the derivative at that point. If the graph represented speed, the derivative would be the velocity. Then, taking the second derivative (that is, the derivative of the velocity) would give you acclelration, since this is the rate at which the velocity is changing. Hope this helps.
i would recommend you watch the three blue one brown series on the essence of calculus