Rush, dash, tear, shoot, charge can all mean to move or cause to move forward with speed.
Rush suggests either impetuosity or intense hurry on account of some exigency, and often carelessness about the concomitant effects of the precipitate action.
Dash is likely to suggest running or moving at a wild unrestrained top speed.
Tear in this sense may suggest extreme swiftness with impetus, violence, and abandon.
Shoot may imply the precipitate headlong rushing or darting of something impelled, as though discharged from a gun.
Charge is likely to suggest a rapid, violent onslaught gathering forceful momentum calculated to overpower.