Drawing Kinematic Graphs for Negatively Accelerating Velocity-Time

[dranseth]

Homework Statement

If we have a velocity-time graph that is negatively accelerating, how would we draw the graph for the acceleration time graph? Would we draw it below zero because it is negatively accelerating (negative number).

The picture of the graph is attached.

The Attempt at a Solution

I drew a linear line below the x-axis to show that the acceleration was negative.

 

[cepheid]

The value of the acceleration at an instant is the value of the slope of the velocity time curve at that instant. Based on that, you can see that the acceleration starts out positive, but it is not constant. The velocity is increasing at an ever decreasing rate, which means that the acceleration is decreasing. At the point where the slope of the v-t graph is zero, velocity hits a maximum, then starts decreasing. This is the point at which the acceleration makes the transition from positive to negative.

 

[dranseth]

so the line for the acceleration-time graph would be linear with a negative slope, then at 0 for a bit when the velocity is constant, then there would be another linear line below the x-axis with a negative slope?

 

[silvashadow]

The graph of the acceleration is the graph of the derivative of the v-graph. Find the slope at each second and graph it onto a new graph. The a-graph is not linear.

 

[cepheid]

Yeah, I never said that it was linear because you can't tell that by inspection. I just said that it was decreasing, that it starts out positive, crosses zero, and becomes negative.