Spatial derivative of velocity

1. What's the derivative of velocity?
2. What is the derivative of velocity with respect to distance?
3. Is the derivative of the velocity function?
4. What is the first time derivative of velocity?

What's the derivative of velocity?

Velocity is the derivative of position with respect to time: v(t)=ddt(x(t)). Acceleration is the derivative of velocity with respect to time: a(t)=ddt(v(t))=d2dt2(x(t)).

What is the derivative of velocity with respect to distance?

In the discussion of the applications of the derivative, note that the derivative of a distance function represents instantaneous velocity and that the derivative of the velocity function represents instantaneous acceleration at a particular time.

Is the derivative of the velocity function?

The velocity is itself the derivative of the position, and so the acceleration is the second derivative of the displacement: a(t)=d2xdt2=¨x(t).

What is the first time derivative of velocity?

By definition, acceleration is the first derivative of velocity with respect to time.