Velocity time graph &instantaneous acceleration

In summary, the instantaneous acceleration of an object whose curve on the velocity-time graph is a straight line can be found by calculating the slope of the line. If the slope is 0, the object is not accelerating and is traveling at a constant velocity. This is because the change in velocity over time, or acceleration, is represented by the slope on a velocity-time graph.
  • #1
karaonstage
1
0
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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  • #2
a=dv/dt.

Acceleration is the gradient of the velocity-time curve at any point.
 
  • #3
acceleration = (velocity 2 - velocity 1)/ (time 2 -time1)
 
  • #4
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).
 
  • #5
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.
 

FAQ: Velocity time graph &instantaneous acceleration

1. What is a velocity-time graph?

A velocity-time graph is a graphical representation of an object's velocity over time. The x-axis represents time and the y-axis represents velocity. The slope of the line on the graph indicates the object's acceleration.

2. How do you interpret a velocity-time graph?

The slope of the line on a velocity-time graph represents the object's acceleration. A steeper slope indicates a higher acceleration, while a flatter slope indicates a lower acceleration. The area under the line on the graph represents the total distance traveled by the object.

3. What is instantaneous acceleration?

Instantaneous acceleration is the acceleration of an object at a specific moment in time. It is calculated by finding the slope of the tangent line to the velocity-time graph at that particular time.

4. How do you calculate instantaneous acceleration from a velocity-time graph?

To calculate instantaneous acceleration from a velocity-time graph, you need to find the slope of the tangent line at the point on the graph that represents the specific time you are interested in. This can be done using the formula: acceleration = change in velocity / change in time.

5. How can you tell if an object is accelerating or decelerating from a velocity-time graph?

If the slope of the line on a velocity-time graph is positive, the object is accelerating. If the slope is negative, the object is decelerating. A flat line with a slope of zero indicates a constant velocity, and no acceleration or deceleration.

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