+234 1) the flight speed of a small bottle rocket can vary greatly, depending on how well its powder burns. Suppose a rocket is launched from rest so that it travels 12.4 m upwards in 2 s. What is the rocket's net acceleration?
2) The shark can accelerate to a speed of 32 km/h in a few seconds. Assume that it takes a shark 1.5 s to accelerate uniformly from 2.8 km/h to 32 km/h. What is the magnitude of the shark's acceleration?
3) In order for the Wright brothers in 1903 flyer to reach launch speed it had to be accelerated uniformly along a track that was 18.3 m long. A system of pulleys and falling weights provided acceleration. If the flyer was initially at rest and it took 2.74 s for the flyer to travel the lenght of the track what was the magnitude of its acceleration?
4) A roller coaster increases the speed of its cars as it raises them to the top of the incline. Suppose the cars move at 2.3 m/s at the base of the incline and are moving at 46.7 m/s at the top of the incline. What is the magnitude of the net acceleration if it is uniform acceleration and takes place in 7 s?
5) A ship with an initial speed of 6.23 m/s approaches a dock that is 255 m away. If the ship accelerates uniformly and comes to rest in 82 s, what is its acceleration?
+154 1) \(d={v_0t}+\frac{1}{2}at^2\\ a_{rocket}=\frac{2d}{t^2}=\frac{2*12.4m}{(2s)^2}=6.2\;m/s^2\)
2)\(a=\frac{\Delta v}{\Delta t}=\frac{32\;km/h\;-\;2.8\;km/h}{1.5s}=\frac{29.2\;km/h}{1.5s}\\ \text{Use dimensional analysis to convert to m/s}^2\\ \frac{29.2\;km/h}{1.5s}*\frac{1h}{3600s}*\frac{1000m}{1km}\approx5.41\;m/s^2\)
3) \(d=v_0t+\frac{1}{2}at^2\\ a=\frac{2d}{t^2}=\frac{2*18.3m}{(2.74s)^2}\approx4.88\;m/s^2\)
4)\(v=v_0+at\\ a=\frac{v-v_0}{t}=\frac{46.7m/s\;-\;2.3m/s}{7s}\approx6.34\;m/s^2\)
5)\(v=v_0+at\\ a=\frac{v-v_0}{t}=\frac{0-6.23m/s}{82s}\approx-0.076\;m/s^2\)
