At time t = 0, a student throws a set of keys vertically upward to her sorority sister, who is in a window at distance h above. The second student catches the keys at time t. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?

Near the end of a marathon race, the first two runners are separated by a distance of 45.0 m. The front runner has a velocity of 3.50 m/s, and the second a velocity of 4.25 m/s. (a) What is the velocity of the second runner relative to the first? (Enter a number. Enter your answer in m/s faster than the front runner.) X m/s faster than the front runner (b) If the front runner is 250 m from the finish line, who will win the race, assuming they run at constant velocity? The first runner will win. The second runner will win. (c) What distance (in m) ahead will the winner be when she crosses the finish line? (Enter a number.) X m

Near the end of a marathon race, the first two runners are separated by a distance of 45.0 m. The front runner has a velocity of 3.45 m/s, and the second a velocity of 4.20 m/s. (a) What is the velocity of the second runner relative to the first? (Enter a number. Enter your answer in m/s faster than the front runner.) m/s faster than the front runner (b) If the front runner is 250 m from the finish line, who will win the race, assuming they run at constant velocity? O The first runner will win. O The second runner will win. (c) What distance (in m) ahead will the winner be when she crosses the finish line? (Enter a number.) m

The velocity of a particle is given by v(t) =t² – 2t. The position of the particle at the time t = 0 is S(0) = 0. 1. Find a formula for the position S(t) at time t. 2. Find the displacement of the object on [0,3]. 3. Find the total distance traveled by the particle on [0,3].