Question

A particle that moves along a straight line has velocity (see below) meters per second after t seconds. How many meters will it travel during the first t seconds?

Answer 1

\[v(t)=t^2e ^{-3t}\]

Answer 2

integrate

Answer 3

I know that, but I might need a little help on the steps.

Answer 4

\[Displacement = \int\limits_{0}^{t} t ^{2} e ^{-3t}dt\]

Answer 5

Remember that \[v(t)=\frac{dx(t)}{dt}\]

Answer 6

If you integrate like kristal said: \[x(t)=\int_0^tv(t)dt\]

Answer 7

\[Distance = \int\limits_{0}^{t}\left| t ^{2} e ^{-3t} \right| dt\]

Answer 8

Do you need help to solve that integral?

Answer 9

I do, I know it's integration by parts. But I don't know which to make f(x) or g(x).

Answer 10

\[\mu = t ^{2}, d \upsilon = e ^{-3t}\]

Answer 11

I think, following LIPET.