Integration of an equation to find displacement

Thread starter AryRezvani
Start date Sep 18, 2012
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Displacement Integration

In summary, integration is a mathematical process used to find the anti-derivative of a function. In physics, it is used to find the total displacement of an object by finding the area under the velocity curve over a given time interval. By integrating the velocity function, we can find the total displacement as the integral represents the change in position. The steps involved in integrating an equation to find displacement include determining the velocity function, integrating with respect to time, and evaluating the integral. Integration can be used for any type of motion as long as the velocity function is known, but it has limitations such as assuming constant velocity and continuous acceleration.

Sep 18, 2012

AryRezvani

Homework Statement

Homework Equations

Above

The Attempt at a Solution

Okay, so I understand I need to integrate the top equation because it's velocity as a function of time.

I just don't know how.

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Sep 18, 2012

Redbelly98

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For starters, the hint is suggesting that you can think of 1.9i as a constant, represented by A.

So, what is [itex]\int A \ dt[/itex] ?

1. What is integration and why is it used to find displacement?

Integration is a mathematical process that involves finding the anti-derivative of a function. In physics, it is used to find the total displacement of an object by finding the area under the velocity curve over a given time interval.

2. How does integration help to find the total displacement of an object?

By integrating the velocity function of an object, we can find the area under the curve, which represents the total displacement of the object. This is because the integral of velocity with respect to time gives us the change in position or displacement.

3. What are the steps involved in integrating an equation to find displacement?

The first step is to determine the velocity function of the object. Then, we integrate the function with respect to time over the given time interval. Finally, we evaluate the integral to find the numerical value of displacement.

4. Can integration be used to find displacement for any type of motion?

Yes, integration can be used to find displacement for any type of motion as long as we have a velocity function that describes the motion. This includes both linear and non-linear motion.

5. Are there any limitations to using integration to find displacement?

Integration can only be used to find displacement in situations where the velocity is known and remains constant over the given time interval. It also assumes that the acceleration is continuous and there are no sudden changes in velocity during the motion.