ok this problem seems easy but it still is giving me problems.
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?
ok this problem seems easy but it still is giving me problems.
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?
Since v(t) > 0 for all t, the particle does not change direction and so the distance travelled after the first t seconds is the same as the displacement x after the first t seconds.
Since $\displaystyle v = \frac{dx}{dt}$ you're expected to calculate $\displaystyle x = \int t^2 e^{-2t} \, dt$. Integration by parts (twice) is one approach that could be used. To get the constant of integration, you can assume x = 0 when t = 0.