The problem involves analyzing the motion of a particle defined by its displacement function x(t) = (t^3 - t^2)e^-t over the interval 0 ≤ t ≤ 9. The goal is to find the velocity v(t) and determine the times when the particle is moving in the positive x direction.
Some participants have provided guidance on analyzing the derivative's sign and suggested plotting the function to visualize where it changes sign. However, there is still uncertainty among participants about the specific steps to take to arrive at the solution.
Participants note the need to consider the factors of the derivative and the implications of the exponential term in the context of determining the sign of the velocity function.
Hybrid_Theory said: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^-tThe 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 said: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.
LCKurtz has given you a starting point.Hybrid_Theory said:... but I'm still at a lose on how to get this. =/
Hybrid_Theory said:The answer is 2-sqrt2 < t < 2+sqrt2 but I'm still at a lose on how to get this. =/