# Homework Help: Find the distance the particle travels

1. Feb 1, 2005

A particle that moves along a straight line has velocity $$v(t)=t^2e^{-3t}$$ meters per second after t seconds. Find the distance the particle travels during the first t seconds.

________________meters (Your answer should be a function of $$t$$)

shouldnt i just integrate that velocity function? cause if you integrate velocity, you get distance right? well i did, but got the wrong answer. here's my answer:

$$-1/27*e^{-3t}(9t^2+6t+2)$$

i also used math programs to integrate the problem just to make i didnt make any mistakes, but it still wont take my answer.

2. Feb 1, 2005

### da_willem

EDIT: Vincentchan is absolutely correct. Choose C so that x(t=0)=0.

Last edited: Feb 1, 2005
3. Feb 1, 2005

### vincentchan

$$-1/27*e^{-3t}(9t^2+6t+2)$$
wrong

the correct one is:
$$-1/27*e^{-3t}(9t^2+6t+2)+C$$

now you need to determine C by the initial condition.... (what is the distance travels when t = 0?)

4. Feb 1, 2005

The thing wrong with your answer: $$-1/27*e^{-3t}(9t^2+6t+2)$$ is that it says that at time t=0 you have traveled -2/27 m. This is because you (and I) forgot the integration constant. You can use this to fix your initial conditions.