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 \(\alpha + \beta\).
×

Problem Loading...

Note Loading...

Set Loading...