LaTeX. Use two #s to start and end the code.brycenrg said:Thank you how do we write like that in this forum?
This equation isn't relevant if the velocity isn't constant.brycenrg said:Homework Statement
Show the area under the curve of v(t) is equal to the displacement from t1 to t2
Homework Equations
x/t = v
Since v(t) = ##\frac{dx}{dt}##, your integral is ##\int_{t_1}^{t_2}v(t) dt = \int_{t_1}^{t_2} \frac{dx}{dt} dt = \int_{t_1}^{t_2} dx##. If you carry that out, what do you get?brycenrg said:The Attempt at a Solution
Integrate V(t) = vt dt
(v/2)*t^2]t1 to t2
(v/2)*t1^2 - (v/2)*t2^2
Not sure if that is good enough or how toactually show it. To find the area you take the integration and v(t) is just the derivative of x(t) but I am not how to show it exactly.
No. In the final integral in Mark's post, the limit variable and integration variable are different: ##\int_{t=t_1}^{t_2}dx##.brycenrg said:thank you guys. You get t2-t1
No. x is a position. What is the position at time t1? (so create one!)brycenrg said:Well isn't x = t1 when t is t1
I thought it was x]t2 upper t1 lower
So it's t2 - t1
No, you can't just plug in arbitrary numbers.brycenrg said:So I could say t1 = 1 and t2 = 2
So then it would be 1 in that case.
So the area would be 1 lol I dono
Yes.brycenrg said:X(t2) - x(t1) is that what they want?
The area under a curve represents the total value or quantity of a variable over a specific range. It is often used to analyze and compare data, as well as to understand the behavior and trends of a particular phenomenon.
The area under a curve is calculated by dividing the curve into small, equal intervals and approximating the area of each interval using a geometric shape, such as rectangles or trapezoids. The sum of these approximated areas gives an estimate of the total area under the curve.
Showing the area under a curve allows for a visual representation of the data, making it easier to understand and interpret. It also provides a more accurate measure of the total value or quantity of a variable compared to just looking at specific data points.
Any continuous curve can have an area under it, including linear, polynomial, logarithmic, and exponential curves. However, discontinuous curves or curves with undefined values cannot have a meaningful area under them.
Yes, the area under a curve can be negative if the curve dips below the x-axis. This indicates that the total value or quantity of the variable over the given range is decreasing or has a negative impact. However, the magnitude of the negative area is still important in understanding the behavior of the variable.