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9. Differential methods
Problem
Solution
The equations of motion of a body travelling in a straight line under the influence of constant acceleration are considered in the Velocity and Acceleration example. These equations can also be expressed in the form of differential and integral calculus functions. This approach is required to solve more realistic mechanics problems where acceleration is non-uniform e.g. where a falling mass is slowed by air resistance which is proportional to its velocity.
Sample problem: mass falling in resistive medium
A particle of mass 1 kg falls vertically from rest from a platform in a medium which exerts a resistive force of v Newtons where v is the speed of the particle (See Fig. 1). Find an expression for the speed and displacement of the particle at any time t.
Solution
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