Kinetics with Veloctiy/Acceleration Problem

[azn1x6flame]

Hello, I need help on this following problem on velocity/acceleration

1. Homework Statement

The velocity function (in meters per second) is given for a particle moving along a line.

v(t)=3t-11, 0 (greater than or equal to) t (greater than or equal to) 5

Find the distance (in meters) traveled by the particle during the given time interval2. Homework Equations

v(t)=3t-11, 0 (greater than or equal to) t (greater than or equal to) 5

3. The Attempt at a Solution

I tried the following:
3(5)-11=4

But it isn't correct, can someone help me with this problem?

I know I have to find the anti-derivative of v(t).

How would I find t? Do I have to do the derivative of v(t) to find acceleration? Would that help me do this problem?

Can someone help me with this problem?

Thanks

 

[ideasrule]

I tried the following:
3(5)-11=4

That's the velocity of the particle at t=5. It's not the total distance travelled.

I know I have to find the anti-derivative of v(t).

How would I find t? Do I have to do the derivative of v(t) to find acceleration? Would that help me do this problem?

The anti-derivative is just the integral. Do you know how to find the integral of a polynomial?

 

[azn1x6flame]

That's the velocity of the particle at t=5. It's not the total distance travelled.
The anti-derivative is just the integral. Do you know how to find the integral of a polynomial?

Yes. This is what I have so far and it's coming up negative:

3/2*t^2-11*t from 0 to 5, so 3/2*25-55 -0 = 125/2-55=-17.5

Whereas the answer book is showing: 137/6

So for some reason, my answer isn't totaling correctly