1. ## distance traveled

A particle that moves along a straight line has velocity $v(t) = t^2e^{-2t}$ meters per second after t seconds. How many meters will it travel during the first t seconds?

2. Originally Posted by viet
A particle that moves along a straight line has velocity $v(t) = t^2e^{-2t}$ meters per second after t seconds. How many meters will it travel during the first t seconds?
integrate v, that will give you s, the formula for the displacement

3. Originally Posted by viet
A particle that moves along a straight line has velocity $v(t) = t^2e^{-2t}$ meters per second after t seconds. How many meters will it travel during the first t seconds?
Originally Posted by Jhevon
integrate v, that will give you s, the formula for the displacement
Since the velocity in this case is always positive my following comment will not change the answer, but it should be mentioned.

To find distance you need to integrate the magnitude of the velocity. ie.
$\Delta s = \int dt \, |t^2 e^{-2t}|$

-Dan

4. Originally Posted by topsquark
Since the velocity in this case is always positive my following comment will not change the answer, but it should be mentioned.

To find distance you need to integrate the magnitude of the velocity. ie.
$\Delta s = \int dt \, |t^2 e^{-2t}|$

-Dan
of course. thank you Dan