Distance traveled by particle

[rahidz2003]

OK, my sister has a particularly tough calc problem, and I got an answer but I'm not sure if it's right.

The problem :

Consider a particle with its distance from the origin given by the function s(t) = t^3 - 3t^2 + t + 3 on the time interval 0<=t<=3. Find the total distance traveled by the particle on the time interval.

I got an answer of about 7.354, but the math was really long and messy, and I'm guessing there's either an easier way or my answer's wrong.

What I did was take the derivative, set it equal to zero, then solved the equation (there were two solutions, one was 0.18 and the other was 1.82). Since s(0) = 3, and s(3) = 6, I did

[s(0.18)-s(0)] + [s(0.18)-s(1.82)] + [s(3)-s(1.82)]. But it's a ton of math to do without a computer, is there any easier method or did I mess up?

Thanks!!!

 

[Deleted member 4993]

As far as I can see - your method is correct.

There are teachers - who would give this type of messy problem as homework - and claim that it builds character.

 

[scrum]

just did it with graphing software on my computer and I got 7.3548