A body with an initial mass of 200Kg is in motion under the action of a constant force of 2000N. Knowing that this body is losing 1 kg of its mass per second and considering that the air resistance is twice its speed and that the body is at rest at time t = 0, then the ordinary differential equation that describes the variation of its speed is given by the image. a. What is the speed of the body v (t) at time t = 1 seconds with 0.5 second intervals, using the Improved Euler method; b. What is the relative percentage error knowing that the particular solution of the PVI is v(t) = 10t− (1/40) * t2.
A body with an initial mass of 200Kg is in motion under the action of a constant force of 2000N. Knowing that this body is losing 1 kg of its mass per second and considering that the air resistance is twice its speed and that the body is at rest at time t = 0, then the ordinary differential equation that describes the variation of its speed is given by the image. a. What is the speed of the body v (t) at time t = 1 seconds with 0.5 second intervals, using the Improved Euler method; b. What is the relative percentage error knowing that the particular solution of the PVI is v(t) = 10t− (1/40) * t2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A body with an initial mass of 200Kg is in motion under the action of a constant force of 2000N. Knowing that this body is losing 1 kg of its mass per second and considering that the air resistance is twice its speed and that the body is at rest at time t = 0, then the ordinary differential equation that describes the variation of its speed is given by the image.
a. What is the speed of the body v (t) at time t = 1 seconds with 0.5 second intervals, using the Improved Euler method;
b. What is the relative percentage error knowing that the particular solution of the PVI is v(t) = 10t− (1/40) * t2.
Transcribed Image Text:PVI v (t) = 200–2u(t).
v(0) = 0
200-t
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