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 $P+Q$