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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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