Velocity-Time Graph: Calculating Instantaneous Velocity

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Discussion Overview

The discussion centers on how to calculate instantaneous velocity and acceleration from a Velocity-Time graph. It includes both conceptual understanding and technical approaches related to interpreting graph data.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that instantaneous velocity at a specific time can be directly read from the Velocity-Time graph as the y-value at that time.
  • Others clarify that if the graph is a position-time graph, the instantaneous velocity would be determined by the slope of the tangent line at that point.
  • There is a suggestion that the acceleration can be calculated as the change in velocity over time, expressed as a = dv/dt.
  • Some participants emphasize the need to find the gradient of the graph at a particular point to determine acceleration.
  • One participant notes that the tangent line may be curved, indicating that acceleration can vary at different points on the graph.

Areas of Agreement / Disagreement

Participants generally agree on the method of reading instantaneous velocity from a Velocity-Time graph, but there is some disagreement regarding the calculation of acceleration, particularly in the context of curved graphs.

Contextual Notes

There are unresolved aspects regarding the definitions of terms and the implications of different graph types (Velocity-Time vs. Position-Time) on the calculations discussed.

bayan
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How do you calculate the instantanius velocity of an object from a Velocity-Time graph?
 
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The instaneous velocity of the object described in the graph at a partycular time t, is simply it's velcoity at that time. In other words you don't have to do any calculus (like you weould have to do if you wished to find the average vellcoity over a certain time) just read the value from the graph.
 
bayan said:
How do you calculate the instantanius velocity of an object from a Velocity-Time graph?

Are you sure this is what you meant? As jcsd pointed out, if you really have a "velocity- time" graph, then the instantaneous velocity is just the "y" value of the graph at time t.

If you have a "position-time" graph, then the velocity is the slope of the tangent line at the point.

If you have a "velocity-time" graph, then the acceleration is the slope of the tangent line.
 
sorry i asked the wrong question.

How do you calculate the Acceleration at a given time?
 
and also the tangent line is curved *the train accelerates at diffrent acceleratio*
 
acceleration: velocity per unit time or V/t. It is just as is as this one.
 
a = dv/dt

i.e. differentiate
 
can you explain abit more please
 
If you only have the graph find the gradient of the grpah at that particular point, if you have the equation differentiate v with respect to t.
 
  • #10
As I said before: if you have a "Velocity-time" graph, draw a tangent to the curve at the given value of t and find its slope.
 

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