Does dx/dt Equal dv or Average Velocity?

[quasi426]

Does dx/dt = dv or just v(avg.)?


Thanks

 

[dextercioby]

There's no average,it's the function itself.

$$v(t)=:\frac{dx(t)}{dt}$$

We call it instant velocity,as we can use the definition of the derivative.We compute the "x" comp.of the velocity at the moment of time $t_{0}$ by

$$v(t_{0})=:\lim_{t\rightarrow t_{0}} \frac{x(t)-x(t_{0})}{t-t_{0}}$$

or simply by plugging the time value in the velocity function itself.

Daniel.

 

[M98Ranger]

for your question! The answer to this question depends on the context and the variables involved. In general, dx/dt represents the rate of change of position with respect to time, while dv represents the rate of change of velocity with respect to time. If we are dealing with a constant velocity, then dx/dt and dv would be the same, as the velocity is not changing. However, if the velocity is changing, then dx/dt would represent the instantaneous velocity at a particular point in time, while v would represent the average velocity over a given interval. So, it's important to specify which variable is being used in the equation and in what context.