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

## $x=-t^{2} e^{-t}-2 t e^{-t}-2 e^{-t}+2$

#### Topics

Integration Techniques

### Discussion

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

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### Video Transcript

The problem is a particle at most. A last ridgeline has lasted. Twenty is equal to squared times interdict reminders for second after two seconds. How far are we willing to try? What your aeons of first? She's like eyes. So this test travel story in the first two seconds? Yes. They caught you into Grew from zero to TV, huh? Be he here? Since we have used this were rebel. You're use another word. Bubbles, Jax. Jax, This this is an integral from zero to explainer. It makes you blacks yaks. With this problem, we can use integration. My parts the foreigner is and through from a to B. You'd have to be prom yaks. See what you have to flee from a toe minus the integral Your prom with the ice. Now for our problems, we can not you, is it? Couldn't you exploiter from this leap with me to connect you, Max? Then you promise different wives released with negative mass. That is integral. Yes, he called to I score halves negative into negative. Ike's ground zero to t minus. And girl, you know you promise? Absolutely. Cities to class. Two acts to make Max next. Thiss think. Aren't you like Auntie and zero to axe? We have. It's ineffective. T squire Ham's into negative t plus two times for this integral. We cannot you use a coach likes on DH from this too. The two Thank us then you promise it would want on. Obviously for you they negative it. Make it Max. This is you Go to two times X times make you be too negative. Attacks from zero toh Teen minus the integral You prom times recent this the class you two make you likes Max. What is this? The contra connective squire To make tea us. Who times back to Teo. Teo. Plus, is this in Minas into negative axe from zero to? Is this the connective squire into your tea? Us right? Minus good. It makes you too. And, Linus, two times you're connected to minus Lauren. This's the distance traveled during the First Cities seconds

WZ

#### Topics

Integration Techniques

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp