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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.
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