Solving for v(t) & x(t) in a Region of Resistive Force

AI Thread Summary
To find v(t) and x(t) for an object experiencing a resistive force of -bv², the relationship between acceleration and velocity must be established, as acceleration a is defined as dv/dt. This leads to the differential equation m dv/dt = -bv², indicating that the acceleration is dependent on the velocity. Solving this differential equation will yield expressions for both velocity and position over time. The discussion emphasizes the need to integrate the equation to find the time variable t in relation to velocity. Ultimately, a mathematical approach to solving the differential equation is necessary to determine the motion of the object under the given resistive force.
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Homework Statement



an object moves to the right with a constant speed v, the ovbject then enters a region where the resistive force is -bv2, find v(t) & x(t)

Homework Equations





The Attempt at a Solution



Fx = ma = -bv2

v = (ma/-b).5

how do i get t in there
 
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You are treating "a" and "v" as independent now.
However, the acceleration is related to the velocity as a = dv/dt.
So your equation is actually:
m dv/dt = - b v2

You are going to have to solve a differential equation.
 
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