find distance covered by object w/ velocity V(t)=20+7cos(t)

[Ken]

It has been years since I've been in school and I am beginning with Calculus I. So, as you might imagine, I have some questions. Some of the problems that I am struggling with are things I should know, it's just coming back slower than I had hoped. Oh, I also Have a calculator that is kicking my rear-end. The problem:

find the distance traveled in 15 seconds by an object moving with a velocity of V(t)=20+7cos(t).

My first inclination is to simply plug the 15 seconds into the equation but I'm not sure what the 20+7cos(t) is doing.

Thanks,

Ken

 

[galactus]

velocity is the derivative of the displacement function. Therefore, the integral of your velocity function should give you displacement. There is a difference between distance and displacement, though.
I am going to assume there's nothing fancy going on here. So we can use

\(\displaystyle \L\\\int_{0}^{15}[20+7cos(t)]dt\)

Can you integrate that?. Very straightforward, but reply if you need more help.

 

[skeeter]

displacement = \(\displaystyle \L \int_{t_1}^{t_2} v(t) dt\)

distance traveled = \(\displaystyle \L \int_{t_1}^{t_2} |v(t)| dt\)

in this particular case, there is no difference between distance traveled (a scalar quantity) and displacement (a vector quantity) since 20 + 7cos(t) > 0 for all t.

displacement and distance traveled are not the same if velocity changes sign anytime during the time interval in question.

point is, be careful to note what the problem specifically asks for.

 

[Ken]

Thank you

Thank you for your help. I don't feel so bad for not being able to solve that one as we are just now being introduced to limits. Differentation and integration are a little later in the course.


Thanks again.