# Calculus problem help?

• Jan 10th 2013, 06:10 PM
achiu17
Calculus problem help?
A wheel has angular position theta = 0 (radians) at t = 0 (seconds). It then rotates with an angular velocity equal to .72t radians/sec. In radians per second, what is the average angular velocity from theta = 4 radians to theta = 9 radians? I got 3 for my answer but I'm not sure if it's right
• Jan 10th 2013, 07:23 PM
chiro
Re: Calculus problem help?
Hey achui17.

Can you show us your working out for this problem?
• Jan 10th 2013, 07:27 PM
achiu17
Re: Calculus problem help?
I found P(t) = .36t^2 radian / sec. I found the times by setting P(t) equal to 9 rad and 4 rad. For 9 rad I got t =5 and for 4 rad i got t = 10/3. I then did (9 rad - 4 rad) / (5 - (10/3)) = 3
• Jan 10th 2013, 08:09 PM
chiro
Re: Calculus problem help?
That looks pretty good.

Finding the average velocity is simply integrating the velocity over a particular region and then dividing by the length of that region (region in this case is time).

Since the anti-derivative of velocity is just displacement (or position), then the integral will be P(5) - P(10/3) and the average just dividing this by (5 - 10/3) which is what you have done.

R confirms your results as well:

> 4/0.36
[1] 11.11111
> 100/9
[1] 11.11111
> 9/0.36
[1] 25