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

Answer 1

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

Velocity is the rate at which a position changes in relation to time; it is the derivative of the position function. The slope of the tangent line indicates the rate of change of a function.

#vecv_(avg)=(Deltas)/(Deltat)#

For an object whose velocity is not constant, the average velocity is not very useful.

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)#

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Answer 2

Amelia Adams

The slope of a distance-versus-time graph represents the speed or velocity of an object.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.