Negative acceleration - change in direction or slowing down?

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SUMMARY

The discussion centers on the interpretation of negative acceleration in physics, specifically whether it indicates a change in direction or deceleration. To determine the nature of negative acceleration, one must analyze both initial velocity (V_i) and final velocity (V_f). A negative acceleration can imply deceleration if the object is moving in the positive direction, or it can indicate an increase in speed if the object is moving in the negative direction. Understanding this requires knowledge of acceleration as the second derivative of the position vector.

PREREQUISITES
  • Understanding of kinematics, including initial and final velocity concepts.
  • Familiarity with the definitions of acceleration and its mathematical representation.
  • Knowledge of derivatives, specifically the second derivative in relation to motion.
  • Basic grasp of vector analysis in physics.
NEXT STEPS
  • Study the relationship between acceleration and velocity in one-dimensional motion.
  • Learn about the implications of negative acceleration in different motion scenarios.
  • Explore the concept of derivatives in physics, focusing on the second derivative and its significance.
  • Investigate vector analysis and its application in understanding motion in multiple dimensions.
USEFUL FOR

Students of physics, educators teaching kinematics, and anyone interested in the principles of motion and acceleration analysis.

kathyt.25
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Homework Statement


Since we can't tell if a value of negative acceleration means a change in direction or decceleration, how WOULD we be able to tell if its a change in direction or the speed is slowing down (say, if we were given v_initial and v_final)?


Homework Equations





The Attempt at a Solution

 
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If you're given V_i and V_f you know that some negative acceleration had to occur in the direction of motion. You need more than just velocities however, to determine much of anything about the acceleration. Similarly, if you're just given an acceleration, that doesn't necessarily tell you much about how the velocity changes.
 
Y'know, a negative acceleration could even mean something is speeding up, if it has a negative velocity (i.e. if it's moving "backwards")
 
I think it has to do with acceleration being the second derivative of the position vector but I am not entirely sure.
 

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