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

1 Answer
Morgan
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, #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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