The storm's strong winds can rush the growth of mold in damp buildings.
A stressful situation can rush an anxiety attack in some individuals.
Excessive caffeine consumption can rush an irregular heartbeat in people sensitive to its effects.
Severe burns can rush the onset of shock if not treated promptly.
Prolonged exposure to cold temperatures can rush the development of hypothermia.

Run with the ball, in football.

Verbs of walking, flying, swimming.

The quarterback will rush the ball down the middle of the field to get past the defenders.
As the running back received the handoff, he began to rush down the sideline to gain a few yards.
The fullback quickly rush forward through the gap and toward the end zone.
To catch the team off guard, the running back decided to rush the ball straight up the middle.
In a last-ditch effort to score, the quarterback chose to rush with the ball instead of throwing a pass.

Urge to an unnatural speed; "Don't rush me, please!".

Verbs of size, temperature change, intensifying, etc..

Cause to move fast or to rush or race; "The psychologist raced the rats through a long maze".

Verbs of walking, flying, swimming.

The taxi driver rushed us through the city to catch our flight on time.
The emergency responders hastened the ambulance to rush the patient to the hospital.
She hurried her children to finish breakfast so they wouldn't miss the school bus.
The organizers forced the competitors to rush through the final round due to time constraints.
The wind turbines were designed to rush large volumes of air through their propellers for maximum energy efficiency.