# Extreme Momentum

At time $$t=0$$, a stationary particle of mass $$m$$ starts to experience a time dependent force $F(t) = \begin{cases} \mathbf{k}t(T-t) & \text{for } 0 \leq t \leq T \\ 0 & \text{for } t \gt T \end{cases}$

where $$\mathbf{k}$$ is a constant vector.

Find the momentum of the particle when the action of the force discontinues.

• If the answer is in the form $$\displaystyle \frac { \mathbf{k}{ T }^{ \alpha } }{ \beta }$$, where $$\alpha$$ and $$\beta$$ are natural numbers, find $$\alpha + \beta$$.
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