Integrating to Find Distance from Velocity

Edward had to escape from prison to work in the HMMT grading room. He stopped to rest at a place distance $1,875$ from the prison and was spotted by a guard with a crossbow. The guard fired an arrow with an initial velocity of $100$. At the same time, Edward started running away with an acceleration of $1$. Assuming that air resistance causes the arrow to decelerate at $1$ and that it does hit Edward, how fast was the arrow moving at the moment of impact?

Source: HMMT February 1998