# Particle in a time varying curve

**Classical Mechanics**Level 5

A particle moves along the curve such that its position vector is given as a function of time as \(\vec{R}=(t^3-4t) \hat { i } +(t^2+4t) \hat { j }+(8t^2-3t^3) \hat { k }\) where \(t\) denotes time. The magnitude of **acceleration** along the normal at time \(t=2\) can be represented as \(P\sqrt{Q}\)

where \(P,Q\) are integers and \(Q\) square free.

Find \(P+Q\)