Question

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

Answer 1

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, `t`, where the instantaneous velocity at time `t` is the slope of the line that is tangent to the position-versus-time graph at time `t`.

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