1. ## Acceleration/ total distance

Hi I was starting a total distance problem and got stuck.

The acceleration of an object is given by a(t) =6sin(t) with initial velocity of -9.5. Find the total distance the object travels on the interval [0, pi] to the nearest integer.

I know to take the integral and solve for velocity. I got the equation v(t) = -6cos(t) - 3.5. Firstly, is that right? and secondly How do I continue from there?

2. velocity function is correct

total distance traveled = $\displaystyle \int_0^{\pi} |v(t)| \, dt$

3. Then am I right in saying that 11 would be the correct answer?

4. no ... not the distance traveled.

the displacement is -11, but in this case, displacement $\displaystyle \neq$ distance traveled

5. Oh so I would have to determine where the object changes direction and add the area from both curves?

6. total distance = $\displaystyle -\int_0^a v(t) \, dt + \int_a^{\pi} v(t) \, dt$

where $\displaystyle a = \arccos\left(-\frac{7}{12}\right)$

7. Okay thank you so much, I have been having problems with that one for a while.