Times when particle is moving in the positive x direction

[Hybrid_Theory]

Homework Statement

A particle has displacement x(t) = (t^3 - t^2)e^-t for times 0=<t=<9.
Find its velocity v(t) and determine for what times the particle is moving
in the positive x direction.

Homework Equations

Differentiating x(t) you get v(t)=-t(t^2-4t+2)e^-t

The Attempt at a Solution

I differentiated the equation but I am lost on how to get the times it is moving in the positive x direction.

 

[LCKurtz]

Homework Statement

A particle has displacement x(t) = (t^3 - t^2)e^-t for times 0=<t=<9.
Find its velocity v(t) and determine for what times the particle is moving
in the positive x direction.

Homework Equations

Differentiating x(t) you get v(t)=-t(t^2-4t+2)e^-t

The Attempt at a Solution

I differentiated the equation but I am lost on how to get the times it is moving in the positive x direction.

You have to determine where the derivative is positive. You do that by analyzing the signs of the factors of the derivative. You may need the quadratic formula to see where that quadratic expression changes sign.

 

[Hybrid_Theory]

The answer is 2-sqrt2 < t < 2+sqrt2 but I'm still at a lose on how to get this. =/

 

[Mark44]

You have to determine where the derivative is positive. You do that by analyzing the signs of the factors of the derivative. You may need the quadratic formula to see where that quadratic expression changes sign.

... but I'm still at a lose on how to get this. =/

LCKurtz has given you a starting point.

 

[Ray Vickson]

The answer is 2-sqrt2 < t < 2+sqrt2 but I'm still at a lose on how to get this. =/

When in doubt, plot a graph (leaving out the exp(-t) factor, which does not change the sign of v(t)). In other words, plot f(t) = -t*(t^2 - 4t + 2) over a range of t values. The plot can be rough; all you really want to know is where f(t) changes sign.

RGV