Finding Values of A, B, and C for Parabolas on a Velocity-Time Graph

[AlchemistK]

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?

 

[Clever-Name]

Since you know some of the values that the parabolas pass through you can set up a series of equations with know Y and X values and solve for A, B, and C

 

[Ray Vickson]

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?

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

 

[AlchemistK]

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

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.
Putting the values of 3 and 5 in the equation, c comes out to be 5/4.
The area of the bottom left curve after integrating, if i am not wrong, comes out to be 10/3.

Am i correct?

 

[Clever-Name]

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?

 

[AlchemistK]

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?

By using the equation of parabola (ax^2 + bx +c) on the three give points at t=6,8 and 10, i can figure out the values of a,b and c, which are, -5/4 , 20 , -50. Right?