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26 September 2014

Mail time: velocity-time graph that crosses the horizontal axis

A correspondent asks:

Hi Greg. I was doing some questions and I'm unsure about a certain response. I'm looking at a velocity vs time graph where the graph is linear and cuts right through the x-axis going in the neg. direction. At EXACTLY the point of intersection do we state that the acceleration is negative because the slope is negative or zero because at that instant the object has zero velocity?

My instincts want me to say negative, but last year I went with zero, sooooooo I'm not really sure.

I've made a graph of what I think you're looking at... see the picture.  You want to know, "What is the direction of the acceleration at point A?"  This is a classic question, with a corresponding classic point of student confusion.  This graph could represent, among other things, a ball thrown upward in free-fall -- it moves upward, slows, stops briefly, and speeds back up toward earth.  

Two ways I'd phrase my answer:

(1) Just because velocity is zero does not mean that acceleration is zero.  Otherwise, gravity would have to turn off just because a ball reaches the peak of its flight.

(2) Acceleration is the slope of a v-t graph.  The horizontal axis isn't special -- the slope of that line doesn't change anywhere, so the acceleration is negative everywhere, both for positive and negative and zero velocities.

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