# Thread: Distance traveled by a particle

1. ## Distance traveled by a particle

I've attached a problem I'm working on, finding displacement is easy in problems like this but I've read through all my notes and whatnot and can't figure out how they're solving the distance traveled by a particle.

2. $\displaystyle d = \int_0^3 |3t - 7| \, dt$

the particle starts out in the negative direction, then changes to a positive direction at t = 7/3

$\displaystyle d = -\int_0^{\frac{7}{3}} 3t - 7 \, dt + \int_{\frac{7}{3}}^3 3t - 7 \, dt$

3. Originally Posted by skeeter
$\displaystyle d = \int_0^3 |3t - 7| \, dt$

the particle starts out in the negative direction, then changes to a positive direction at t = 7/3

$\displaystyle d = -\int_0^{\frac{7}{3}} 3t - 7 \, dt + \int_{\frac{7}{3}}^3 3t - 7 \, dt$
Wait so I don't have to use the antiderivative of 3t-7 at all? I'm still confused, I already got as far as you just said and that's where I stopped due to confusion?

4. Originally Posted by fattydq
Wait so I don't have to use the antiderivative of 3t-7 at all? I'm still confused, I already got as far as you just said and that's where I stopped due to confusion?
yes, you have to use the antiderivative ... twice.

you have two definite integrals to evaluate.

5. OK for the first I got -8.1666667 and the second I got 2/3 and I added the two and it still says it's wrong. And yes I did negate the first term

6. Nvm I got it, thanks man