The discussion revolves around finding the coefficients A, B, and C for the equations of two parabolas represented on a velocity-time graph, with the goal of calculating total displacement from t=0 to t=10 using integration.
Some participants have offered guidance on how to approach determining the coefficients by analyzing the graph's features and using known points. There is a recognition of the need to consider multiple points for each parabola to fully define their equations.
Participants note the initial conditions, such as the velocity being zero at t=0, and discuss the implications of these conditions on the equations of the parabolas. There is an emphasis on using integration to find areas under the curves for displacement calculations.
Look at the bottom-left parabola v = a + b*t + c*t^2. Looking at the graph, what is the value of v when t = 0? What does that say about a, b and c? What is the slope of the graph v at t = 0? What does that say about a, b and c? Finally, you have another point on the graph. That tells you more about a, b and c. You now have enough to determine the graph completely. Do something similar for the right-hand parabola, namely: use the fact that you have three points on the graph, so you can determine the three constants.AlchemistK said:Homework Statement
The graph in the attached file is a velocity-time graph.
We have to find the total displacement from t=0 to t=10.
I know that integration will be used for this problem, and i know my formulas but i do not know of how to form the equation of the two parabolas here.
I know it is of the form Ax^2 + Bx + C but how do i figure out the A.B and C?
At t = 0, the velocity is 0 and so is the slope, right? And i forgot to mention but the initial velocity is 0 so, the equation for the parabola there should be cx^2 because the vertex is at the origin.Ray Vickson said:Look at the bottom-left parabola v = a + b*t + c*t^2. Looking at the graph, what is the value of v when t = 0? What does that say about a, b and c? What is the slope of the graph v at t = 0? What does that say about a, b and c? Finally, you have another point on the graph. That tells you more about a, b and c. You now have enough to determine the graph completely. Do something similar for the right-hand parabola, namely: use the fact that you have three points on the graph, so you can determine the three constants.
RGV
Clever-Name said:Looks right to me. Now what about the 2nd parabola? Another method you can try is putting it in vertex form since you can see where the vertex is, do you remember how to do that?