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- https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Differential_Calculus/Differential_Calculus_(Guichard)/Applications%3A_Free_Falling_BodiesThis is read as, the force required to accelerate a body is directly related to its mass and the magnitude of the acceleration of the mass. For example if a car is traveling down the highway at 82 mph...This is read as, the force required to accelerate a body is directly related to its mass and the magnitude of the acceleration of the mass. For example if a car is traveling down the highway at 82 mph, suddenly sees a cop, and then steps on the pedal, accelerating the cart at 3 mph/s, then its velocity at any time t, were t is measured as soon as he steps on the gas is:
- https://math.libretexts.org/Bookshelves/Differential_Equations/A_First_Course_in_Differential_Equations_for_Scientists_and_Engineers_(Herman)/01%3A_First_Order_ODEs/1.01%3A_Free_FallIn this chapter we will study some common differential equations that appear in physics. We will begin with the simplest types of equations and standard techniques for solving them We will end this pa...In this chapter we will study some common differential equations that appear in physics. We will begin with the simplest types of equations and standard techniques for solving them We will end this part of the discussion by returning to the problem of free fall with air resistance. We will then turn to the study of oscillations, which are modeled by second order differential equations.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Street-Fighting_Mathematics%3A_The_Art_of_Educated_Guessing_and_Opportunistic_Problem_Solving_(Mahajan)/01%3A_Dimensions/1.02%3A_Newton_mechanics-_Free_fallBecause the height is h feet, the variable h does not contain the units of height: h is therefore dimensionless. (For h to have dimensions, the problem would instead state simply that the ball falls f...Because the height is h feet, the variable h does not contain the units of height: h is therefore dimensionless. (For h to have dimensions, the problem would instead state simply that the ball falls from a height h; then the dimension of length would belong to h.) A similar explicit specification of units means that the variables g and v are also dimensionless. The strongest constraint is that the combination of g and h, being a speed, should have dimensions of inverse time (\(T^{−1}\)).
