# Using calculus, how do I go from Acceleration as a Function of Velocity to v(t) to t(d)?

I'm hoping for a physics and/or math genius to help me out here. I need to solve the following problem, and I know very little about calculus.
A bullet fired from a rifle starts traveling with an initial muzzle velocity of 905 m/s. Its rate of (negative) acceleration due to drag as it travels through the...
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I'm hoping for a physics and/or math genius to help me out here. I need to solve the following problem, and I know very little about calculus.

A bullet fired from a rifle starts traveling with an initial muzzle velocity of 905 m/s. Its rate of (negative) acceleration due to drag as it travels through the air is a(v) = -kv^2, where k is a constant and v is instantaneous velocity. Using this information, is it possible to find the equation for velocity as a function of time? From there, is it possible to find the equation for time as a function of displacement?

Ultimately, I need to be able to determine how long it will take the bullet to travel a given distance where initial velocity is known and a(v) = -kv^2.

A bullet fired from a rifle starts traveling with an initial muzzle velocity of 905 m/s. Its rate of (negative) acceleration due to drag as it travels through the air is a(v) = -kv^2, where k is a constant and v is instantaneous velocity. Using this information, is it possible to find the equation for velocity as a function of time? From there, is it possible to find the equation for time as a function of displacement?

Ultimately, I need to be able to determine how long it will take the bullet to travel a given distance where initial velocity is known and a(v) = -kv^2.

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