Can't seem to integrate this rectilinear motion equation.

AI Thread Summary
The discussion focuses on solving a rectilinear motion problem involving the equation v = 1/6(t(60 - t)). The user initially finds the stationary points but struggles with simplifying the equation for integration. They express difficulty in integrating due to the presence of fractions. Responses clarify that integrating involves adjusting the powers of t and handling constants correctly. The conversation concludes with the user gaining clarity on integrating variables with coefficients and fractions.
MegaDeth
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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.
 
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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!
 
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