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I'm having trouble finding the relation between velocity and time given this formula. If anyone has a solve for this, It would be great if you took your time to help me as I know this includes differential acceleration, which requires calculus. As velocity increases, drag force increases - until terminal velocity.

F=1/2 * p * v^2 * C * A

p is density of fluid and is set to 1.225 kg/m^3

v is velocity of object relative to fluid

C is Coefficient of Drag and is set to 0.9, as my shape is a sphere

A is cross-sectional area which is π/4, as it is the "CS" of a sphere where diameter of "CS" circle in sphere is 1.

From my knowledge, I was only able to proceed this far:

Lets assume 1/2 * p * v^2 * C * A=ma1

Lets assume k=1/2pC (A is not included because I'll be comparing graphs with different values for A)

F=ma is the Net Force

g=9.80665m/s/s

F=mg

mg-ma1=ma

Force of gravity-Force of Drag=Net Force.

mg - 1/2 * k * v^2 * A = ma

g - (1/2 * k * v^2 * A) / m = a

How do I proceed? Do I differentiate a for dv/dt and integrate it later? I suck at calculus and I don't understand much of its logic, please help. If you have extra time, please give me a graph for velocity given time and acceleration given time.

Q: How do I solve this calculus problem regarding drag force and gravity?

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Gravity is a force, which means that it has a corresponding acceleration (rate of rate of change). Because calculus is the study of rates of change, accelerations are studied in calculus.

no he created the laws of force

He invented calculus (Leibnitz in Germany also invented it). Newton used calculus to show that the curved path of a planet's orbit is due to the inward acceleration of the planet towards the Sun, which is exactly balanced by the inward force of gravity at every instant. This enabled him to explain Kepler's law of planetary motion in terms of the new theory of particle dynamics.

Force or weight Force= mass X acceleration gravity is an acceleration (9.8m/s2) Weight = mass X acceleration due to gravity

Yes, there can be negative gravity. If a gravity is a pulling force then in the other hands a negative gravity would be a pushing force, in other words, the negative gravity would push us to wherever and the positive gravity on Earth would pull us.

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Gravity is a force, which means that it has a corresponding acceleration (rate of rate of change). Because calculus is the study of rates of change, accelerations are studied in calculus.

The best answer is: Because that's the way gravity works. If you take Newton's brief, simple formula for the force of gravity, and massage it with calculus and geometry, it turns out that every closed gravitational orbit must be elliptical.

what is the force of gravity on mecury

Gravity is a force but has no mass.

gravity not as a force, but as the curvature of spacetime

no he created the laws of force

Discoveries of Newton include: Calculus, binomial expansion, uses of logarithms and making very accurate log tables, the laws of motion, the law of universal gravitation, properties of light, 'proof' of Kepler's laws, ... If you can find it, there is a book, "Biorgaphy of Physics" by George Gamow. It is about 350 pages and Newton has his own chapter of over 60 pages. Read it to find out more on Newton.

None. Gravity IS the force in this case.

Gravity Force was created in 1989.

Gravity Force happened in 1989.

Gravity is a type of force.

gravity is a force by which objects are attracted to the centre of.