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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.
What else can I help you with?
What is the relation of gravity with calculus?
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.
Did Newton create calculus?
no he created the laws of force
What did isaac newton accomplish in calculus?
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.
What is mass multiplied by gravity?
Force or weight Force= mass X acceleration gravity is an acceleration (9.8m/s2) Weight = mass X acceleration due to gravity
Can their be negative 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.
