# Can't seem to integrate this rectilinear motion equation.

In summary, the conversation discusses finding the distance between t = 0 and t = 60 for an object with the equation v = 1/6(t(60 - t)). The first step is to find the values of t where the object is stationary, and then to simplify the equation for integration. The formula for integrating variables with coefficients and fractions is also discussed.
Hi, so I have a question where it asks me to find the distance between t = 0 and t = 60 for the equation v = 1/6(t(60 - t)). First I had to find the values of t which the object moving was stationary, that was simple enough. (It's been around a month and a half since I did rectilinear motion). It then asks me to to find the distance between t = 0 and t = 60. I'm having somewhat trouble simplifying the equation ready for integrating. This is my try at it:

v = 1/60(t(60 - t))
v = t - t2/60

After this, I'm stuck, it's been too long since I've done any real maths... I'm not sure, all I need is an equation without fractions so it's easy enough to integrate.

Do you know how to integrate the first part?
The integral of t (with respect to t)
add 1 to the power, divide by the new power.

For the second part, the part that includes the fraction, this fraction (-1/60) is just a constant. So, integrate t^2 then simply place the constant (-1/60) in front of it.
Remember, to integrate t^2 (with respect to t), you simply add 1 to the power (here the power is 2) then divide by the new power.

Then combine the answers of the 2 integrals (t and -1/60 t^2) and don't forget to add the constant of integration.

e.g. the integral of t^3/2 is (t^4/4)/2=t^4/8+constant.

Oh god, of course. I never did do many integratation including fraction, thanks for clearing that up for me though. So whenever you integrate a variable with a coefficient what a fraction, you simply integrate the variable and switch the fraction around and multiply it. Thanks a lot!

## 1. What is rectilinear motion?

Rectilinear motion is the motion of an object in a straight line, either horizontally or vertically, with constant speed.

## 2. What is the equation for rectilinear motion?

The equation for rectilinear motion is x = x0 + v0t + 1/2at2, where x is the final position, x0 is the initial position, v0 is the initial velocity, t is time, and a is acceleration.

## 3. Why can't I seem to integrate the rectilinear motion equation?

Integrating the rectilinear motion equation can be difficult for some people because it requires a good understanding of calculus and the proper techniques for integration. If you are having trouble, it may be helpful to seek out a tutor or review your calculus skills.

## 4. How do you solve for the acceleration in a rectilinear motion problem?

To solve for acceleration in a rectilinear motion problem, you can use the equation a = (v - v0)/t, where v is the final velocity and v0 is the initial velocity. Alternatively, you can use the kinematic equation a = 2(x - x0 - v0t)/t2.

## 5. Can the rectilinear motion equation be used for non-constant acceleration?

Yes, the rectilinear motion equation can be used for non-constant acceleration as long as the acceleration is known at every point in time. In this case, the equation becomes x = x0 + v0t + 1/2∫a(t)dt, where a(t) is the acceleration function.

• Mechanics
Replies
4
Views
882
• Mechanics
Replies
4
Views
682
• Mechanics
Replies
49
Views
1K
• Mechanics
Replies
3
Views
2K
• Mechanics
Replies
11
Views
1K
• Mechanics
Replies
3
Views
5K
• Mechanics
Replies
25
Views
1K
• Mechanics
Replies
5
Views
859
• Mechanics
Replies
8
Views
993
• Introductory Physics Homework Help
Replies
4
Views
755