MooreLikeMike
New member
- Joined
- Nov 10, 2020
- Messages
- 13
Hi everyone,
I have the question: "Suppose the velocity of a car is given by v(t) = 1/(2t+1)+(4t+3)^2 feet per second. How far does the car travel in the first two seconds?"
I know that v(t) is the derivative of the equation for the distance traveled, I'll just call it D(t). So to find D(t), I need to find the indefinite integral of v(t). Then after finding D(t) = 1/2ln(abs(2t+1))+1/12(4t+3)^3+C, I should set "t" equal to zero and solve for "C" to find D(t).
But where I'm confused is because I know if the question were to ask to find "how far does the car travel in 3 to 6 seconds", I would find the definite integral from 3 to 6 and that would be the answer. But since the question that I'm given asks to find the distance in the first 2 seconds, I not sure if I'm supposed to find the definite integral from 0 to 2, or if I should just plug 2 in for "t" and solve it that way.
Because if I find the definite integral from 0 to 2, "C" will be eliminated, but if I don't, "C" will still be apart of the answer.
I have the question: "Suppose the velocity of a car is given by v(t) = 1/(2t+1)+(4t+3)^2 feet per second. How far does the car travel in the first two seconds?"
I know that v(t) is the derivative of the equation for the distance traveled, I'll just call it D(t). So to find D(t), I need to find the indefinite integral of v(t). Then after finding D(t) = 1/2ln(abs(2t+1))+1/12(4t+3)^3+C, I should set "t" equal to zero and solve for "C" to find D(t).
But where I'm confused is because I know if the question were to ask to find "how far does the car travel in 3 to 6 seconds", I would find the definite integral from 3 to 6 and that would be the answer. But since the question that I'm given asks to find the distance in the first 2 seconds, I not sure if I'm supposed to find the definite integral from 0 to 2, or if I should just plug 2 in for "t" and solve it that way.
Because if I find the definite integral from 0 to 2, "C" will be eliminated, but if I don't, "C" will still be apart of the answer.