Calculus Problem: Solving for t Given x=6.1

  • Thread starter jeremy5561
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    Calculus
Your acceleration is a function of time, so you can't use it.In summary, the conversation discusses a problem involving a function with variables for acceleration, time, and distance. The individual has attempted to solve for time and has obtained a value of 2.45175, but is questioning the accuracy of this solution when using the formula for average acceleration. It is determined that this formula is only valid for constant acceleration, and since the acceleration in this problem is a function of time, it cannot be used. Therefore, the solution may not be correct.
  • #1
jeremy5561
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Homework Statement


Well I've pretty much boiled the problem down to this:

Let a = 1.767+0.3213t
v(0)=0
x(0)=0

then I got
x(t)=(0.8835+0.05355 t) t^2

Given x=6.1

Solving for t I got t=2.45175

But I'm just curious. If I calculate average acceleration I get a_av=2.16.

If I now apply x=1/2at^2 using a average I don't get 6.1

Homework Equations


Using calculus I turned a=1.767+0.3213t to
x=(0.8835+0.05355 t) t^2

Given x is 6.1 I solve t=2.45175


The Attempt at a Solution



But now when I use the average velocity trick and then use x= 1/2at^2 I don't get 6.1. Is my solution incorrect?
 
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  • #2
Your acceleration is a function of time. The average acceleration won't give you the correct distance traveled.
 
  • #3
jeremy5561 said:
If I now apply x=1/2at^2 using a average I don't get 6.1
That formula is only valid for constant acceleration.
 

1. How do I solve for t given x=6.1?

To solve for t, we need to use the formula t = x/c, where c is the constant. In this case, c is the constant 6.1. Substitute the value of x and c into the formula and solve for t.

2. Can I use a calculator to solve this calculus problem?

Yes, you can use a calculator to solve the problem. Simply input the values of x and c into the formula t = x/c and the calculator will give you the answer.

3. Do I need to know any specific calculus concepts to solve this problem?

Yes, you need to have a basic understanding of derivatives and the concept of inverse functions to solve this problem.

4. What if the value of x is negative?

If the value of x is negative, the formula t = x/c still applies. However, the answer for t will also be negative. Make sure to pay attention to the sign of the answer.

5. Can I solve this problem without using the given formula?

Yes, there are other methods to solve for t without using the given formula. However, the formula t = x/c is the simplest and most efficient way to solve this problem.

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