A particle is moving along a straight line such that its acceleration is defined as a = (-2v) m/s^2, where v is in meters per second. If v = 20 m/s when s = 0 and t = 0, determine the particle’s position, velocity, and acceleration as functions of time.

Question

A particle is moving along a straight line such that its acceleration is defined as a = (-2v) m/{ s }^{ 2 }, where v is in meters per second. If v = 20 m/s when s = 0 and t = 0, determine the particle’s position, velocity, and acceleration as functions of time.

Accepted Answer

[latex]a = -2v \ \frac { dv } { dt } = -2v \ \int_{ 20 }^{ v } { \frac { dv } { v } } = \int_{ 0 }^{ t } { -2\space dt } \ ext{ ln } \frac { v } { 20 } = -2t \ v = ( { 20e }^{ -2t } ) ext{ m/s } \ a = \frac { dv } { dt } = ({ -40e }^{ -2t }) m/{ s }^{ 2 } \ \int_{ 0 }^{ s } { ds } = v\space dt = \int_{ 0 }^{ t } { ({ 20e }^{ -2t })dt } \ s = { -10e }^{ -2t }|_{ 0 }^{ t } = -10({ e }^{ -2t } - 1) \ s = 10(1 - { e }^{ -2t }) ext{ m }[/latex]

Question : A particle is moving along a straight line such that its acc...

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