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1D Dynamics

A variety of phenomena can be captured by simplistic 1-dimensional models. Learn the essentials of mechanical motion in this stripped-down setting.

Problem Solving

A ball starts to free-fall from a height of \(5.4\text{ m}.\) At the point when the ball is \(3.3\text{ m}\) above the ground, what is the approximate velocity of the ball?

The gravitational acceleration on earth is about \(9.8\text{ m/s}^2.\)

A 100 gram cylindrical glass is attached to a string that hangs from the ceiling. Then the glass which has a cross-sectional radius of 4 cm and a height of 15 cm, is slowly filled with water. If the string breaks when the glass is 2/3 full, what is the maximum tension in Newtons that the string can support?

Details and assumptions

  • The acceleration of gravity is \(-9.8\text{ m/s}^2.\)
  • The density of water is \(1\text{ g/cm}^3.\)

An object is vertically thrown to the sky from the ground with an initial velocity of \(7.2\text{ m/s}.\) Approximately how long does it take in seconds for the object to fall back to the ground?

The acceleration of gravity on earth is about \(g=9.8\text{ m/s}^2.\)

An airplane is taxiing on a straight runway for takeoff with a constant acceleration. At time \(t=11.5\text{ s}\) the plane has a velocity of \(127\text{ km/h}, \) and at time \(t=15.5\text{ s}\) the plane's velocity is \(152\text{ km/h}.\) Find the approximate acceleration of the plane.

An advanced humanoid robot is running a marathon with a constant velocity of \(7.7\text{ m/s}.\) Near the finish line, it starts to accelerate with a constant acceleration of \(0.70\text{ m/s}^2\) for \(74 \text{ s}\) until it reaches the finish line. What was the robot's approximate distance from the finish line when it started to accelerate?

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