How to find Instantaneous acceleration with points from a graph

In summary, to find instantaneous acceleration when given final velocity, initial velocity, final time, and initial time, you can use the equation v = u + at or find the slope of the graph of uniform acceleration.
  • #1
adamgriffis
1
0

Homework Statement



How to find instantaneous acceleration when the velocity final is 4 m/s, the velocity initial is 1 m/s, the time final is 5 seconds, and the time initial is 2 seconds?

Homework Equations





The Attempt at a Solution


I have no idea how to do the second derivative for the equation


 
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  • #2
adamgriffis said:
How to find instantaneous acceleration when the velocity final is 4 m/s, the velocity initial is 1 m/s, the time final is 5 seconds, and the time initial is 2 seconds?
Hi adamgriffis! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

Since you haven't included a graph, it's reasonable to assume this is a question involving straight-line motion under constant acceleration. For such motion, there is a set of equations with which you must become adept because you will rely on them for further study.

Have you encountered an equation, or one similar to: v = u + a·t https://www.physicsforums.com/images/icons/icon5.gif [Broken]
 
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  • #3
Though I can't be 100% sure, I'm going to assume that the graph you have mentioned is a v vs. t graph of uniform acceleration. There are a number of ways to determine the instantaneous acceleration between the points you listed, which would be (2, 1) and (5, 4). The first would be NascentOxygen's excellent suggestion to use v = u + at (final velocity = initial velocity + acceleration * time), and solve for the acceleration.

The second way is useful in graphs. This only works with straight-line graphs.* Assuming that the slope between the two points you listed is constant and unchanging, solving for the slope (slope = change in y divided by change in x) will yield the instantaneous acceleration at any time between those two points. If you want to know why, when an object moves at constant velocity/acceleration, its average and instantaneous velocities/accelerations are equal at all times.

Hope this helped.

*Note: If you have a curve plotted on a graph, it is possible to use this slope method again. Since instantaneous acceleration is defined as the change in velocity as the limit of change in time approaches zero, getting two points as close as possible to the point of acceleration you are trying to find will yield a good estimate. A more exact result would come from plotting a line tangent to the point of acceleration.
 

1. How do I determine the instantaneous acceleration from a graph?

To find the instantaneous acceleration from a graph, you need to calculate the slope of the tangent line at a specific point on the graph. This can be done by finding the derivative of the function represented by the graph. The derivative at a point will give you the instantaneous rate of change, which is equivalent to the instantaneous acceleration at that point.

2. What is the formula for finding the slope of a tangent line on a graph?

The formula for finding the slope of a tangent line on a graph is the derivative of the function at a specific point. This can be represented as dy/dx, where y is the function and x is the independent variable. Alternatively, you can also use the formula (f(x+h) - f(x)) / h, where h is a very small value approaching 0.

3. Can I find the instantaneous acceleration at any point on the graph?

Yes, you can find the instantaneous acceleration at any point on the graph as long as you have the necessary information to calculate the derivative at that point. This includes the function, the independent variable, and the point at which you want to find the acceleration.

4. How do I interpret the instantaneous acceleration from a graph?

The instantaneous acceleration at a specific point on a graph represents the rate of change of the velocity at that point. It tells you how quickly the velocity is changing at that exact moment. A positive acceleration indicates an increase in velocity, while a negative acceleration indicates a decrease in velocity.

5. Can I use a graph to find the average acceleration over a certain time interval?

Yes, you can use a graph to find the average acceleration over a certain time interval by finding the slope of the secant line that connects the two points on the graph representing the beginning and end of the time interval. This is calculated using the formula (f(b) - f(a)) / (b - a), where a and b are the values of the independent variable at the beginning and end of the time interval, respectively.

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