# What does the slope of a distance-versus-time graph represent?

##### 1 Answer

Jan 1, 2017

The slope of a position-versus-time graph represents the velocity.

#### Explanation:

The slope of the tangent line represents the rate of change of a function. Velocity is the rate of change of position with respect to time. Equivalently, velocity is the derivative of the position function.

#vecv_(avg)=(Deltas)/(Deltat)# The average velocity has limited usefulness for an object whose velocity is not constant.

We can define an object's instantaneous velocity at a single instant of time,

#vecv=lim(Deltat->0)(Deltas)/(Deltat)=(ds)/(dt)#