Velocity time graph &instantaneous acceleration

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Homework Help Overview

The discussion revolves around finding instantaneous acceleration from a velocity-time graph, particularly when the graph is represented as a straight line. The subject area includes concepts of kinematics and graphical analysis of motion.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between the slope of a velocity-time graph and instantaneous acceleration. Questions arise about the implications of a straight line on the graph and how it relates to acceleration.

Discussion Status

There is an ongoing exploration of how to interpret the slope of the velocity-time graph as a measure of acceleration. Some participants provide insights into the mathematical relationship between velocity and acceleration, while others reiterate the importance of understanding the concept of acceleration itself.

Contextual Notes

Participants note that the graph being a straight line implies certain characteristics about the object's motion, such as constant velocity or zero acceleration, but the discussion remains open-ended regarding the implications of these observations.

karaonstage
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How can you find the instantaneous accelertation of an object whose curve on the velocity-time graph is a straight line?
 
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a=dv/dt.

Acceleration is the gradient of the velocity-time curve at any point.
 
acceleration = (velocity 2 - velocity 1)/ (time 2 -time1)
 
karaonstage said:
How can you find the instantaneous accelertation of an object whose curve on the velocity-time graph is a straight line?

Only just a straight line? Then
[tex]\forall n > 1,\;\frac{{d^n v}}{{dt^n }} = 0[/tex]
over the interval containing this line

*karaonstage, simply find the slope of this line, and you will thus calculate the acceleration of the object.
If the slope [itex]= 0[/itex], the object simply doesn't accelerate (travels at constant velocity).
 
Above is correct. But next time, try to think to yourself, what is acceleration. Change in velocity over time, well, if you have a velocity vs time graph, than a change in velocity over time IS your slope.
 

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