Sample Linear Kinematics Problems

1. A runner accelerates at 12.4 m/s² for 0.5 seconds. If her final velocity is 9.7 m/s, what was her initial velocity?

2. How much time will a batter have to decide to swing at a 90 mph pitch released 56 feet from the plate if it takes him 0.3 seconds to actually swing the bat?

3. The luge track at the Utah Olympic Park is 1316 m in length. The altitude at the start of the track is 2237 m; altitude at the end is 2205 m. If a luger takes 48 seconds to complete a run, what is his average speed? Average vertical velocity? [speed = 27.4 m/s, v_y = -0.667 m/s]

4. In Stage 10 of the 2000 Tour de France, Lance Armstrong captured the overall lead with an impressive climb to the finish line at Lourdes-Hautacam, elevation 1560 m. Armstrong made the 13.5 km climb in 36 minutes. Calculate his average speed. [6.25 m/s]. If the altitude at the base of the climb was 493.5 m, what was his average vertical velocity? [v_y = 0.49 m/s]

5. Being the daring soul that you are, you take your roommates up on a dare to take a bobsled ride. The closest bobsled track is in Utah, so you take a road trip. The bobsled track at the Utah Olympic Park is 1340 m long. You complete the run in 63 seconds. What is your average speed? [21.3 m/s]