A particle of mass m moves in a straight line wih velocity v(t), subject only to a linear air resistance F = -1mv. Assume the particle starts with velocity u in x = 0. dv dt 1. Using the change of variables = 21 find the velocity of the particle as a function of its position, x, the initial velocity, u, and its mass, m. dv dx v(x) = 2. Calculate the distance à travelled by the particle before coming to a stop. x =

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A particle of mass m moves in a straight line wih velocity v(t), subject only to a linear air resistance F = -1mv. Assume the particle starts with velocity u in x = 0.
dv
1. Using the change of variables = V-
dt
v(x) =
du, find the velocity of the particle as a function of its position, a, the initial velocity, u, and its mass, m.
dx
2. Calculate the distance travelled by the particle before coming to a stop.
ΕΠΙΣ
î=
Transcribed Image Text:A particle of mass m moves in a straight line wih velocity v(t), subject only to a linear air resistance F = -1mv. Assume the particle starts with velocity u in x = 0. dv 1. Using the change of variables = V- dt v(x) = du, find the velocity of the particle as a function of its position, a, the initial velocity, u, and its mass, m. dx 2. Calculate the distance travelled by the particle before coming to a stop. ΕΠΙΣ î=
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