A particle's position is r(vector) =(ct^2−2dt^3)i^+(2ct^2−dt^3)j^,
where c and d are positive constants. Find expressions for times t 0 when the particle is moving in the x-direction.
Express your answer in terms of the variables c and d.
can anybody walk me through how to even approach this problem? I am totally lost.

Question

A particle's position is r(vector) =(ct^2−2dt^3)i^+(2ct^2−dt^3)j^, 
where c and d are positive constants. Find expressions for times t > 0 when the particle is moving in the x-direction.
Express your answer in terms of the variables c and d.
can anybody walk me through how to even approach this problem? I am totally lost.

theeric · Answer

Hmm... Well, you can take the derivative of the $\hat i$ component with respect to $t$ to find the horizontal velocity! Is that what it is asking?

If it specifies "positive $x$ direction," we'd set the $\hat i$ component's magnitude to be greater than $0$, and then solve for $t$. You'd have to use the quadratic formula, I think!