A race car can accelerate from rest to incredible speeds. In one case, a dragster is able to finish the \(305 \mathrm{~m}\) run in \(3.64 \mathrm{~s}\) (and it continues to accelerate throughout this time)! What was the magnitude of the average acceleration during this run? What is the top speed of the dragster?
The maximum acceleration that feels comfortable for passengers in a train is \(1.2 \mathrm{~m/s^2}\text{.}\) Suppose that train’s route includes two adjacent stations (stops) that are just \(800 \mathrm{~m}\) apart. What is the fastest speed the train could attain between the stations and still pick up and drop off passengers at both? What is the shortest time between the stations?
A diver bounces straight up from a diving board and (avoiding the diving board on the way down) falls feet first into a pool. She leaves the board with a velocity of \(4.00 \mathrm{~m/s}\text{,}\) and her takeoff point is \(1.80 \mathrm{~m}\) above the pool. How long are her feet in the air? What is her speed when her feet hit the water? What is her highest point above the board?
Two rugby players start from rest, \(46 \mathrm{~m}\) apart. Each player runs directly toward the other, both of them accelerating. Player 1’’’s acceleration magnitude is \(0.60 \mathrm{~m/s^2}\text{.}\) Player 2’s acceleration magnitude is \(0.40 \mathrm{~m/s^2}\text{.}\) How much time passes before the players collide? At the instant they collide, how far has player 1 run? Assuming player 1 is traveling in the positive \(x\)-direction, what is the displacement of player 2 in the \(x\)-direction?
A frog leaps from level ground with a speed of \(2.00 \mathrm{~m/s}\) at an angle \(40.0^o\) up from the horizontal. Unlike usual, use the more precise value \(g = 9.81 \mathrm{~m/s^2}\text{.}\) What is the time of flight for the frog? What is the range of the frog’s flight? What is the max height the frog achieves?
