Question

The (only) force on a object moving in one dimension is given by [ F=-frac{P}{V+v} ] where ( P ) and ( V ) are positive constants, and ( v ) is the speed of the particle. The particle is moved to a distance ( b ) from the origin, and released with zero initial velocity. (a) What are the dimensions or SI units of ( V ) ? (b) What are the dimensions or SI units of ( P ) ? (c) Write Newton's second law for the object, in a form that involves only constants, ( v, x ), and derivatives involving only ( v ) and ( x ). (d) By direct integration from the previous equation, find ( x(v) ) for the particle. Note: Do not try to invert this to find ( v(x) ) ! Hint: you are not asked to find ( v(t) ) or ( x(t) ).

          The (only) force on a object moving in one dimension is given by
[
F=-frac{P}{V+v}
]
where ( P ) and ( V ) are positive constants, and ( v ) is the speed of the particle. The particle is moved to a distance ( b ) from the origin, and released with zero initial velocity.
(a) What are the dimensions or SI units of ( V ) ?
(b) What are the dimensions or SI units of ( P ) ?
(c) Write Newton's second law for the object, in a form that involves only constants, ( v, x ), and derivatives involving only ( v ) and ( x ).
(d) By direct integration from the previous equation, find ( x(v) ) for the particle. Note: Do not try to invert this to find ( v(x) ) ! Hint: you are not asked to find ( v(t) ) or ( x(t) ).

$The (only) force on a object moving in one dimension is given by [ F=-fracPV+v ] where ( P ) and ( V ) are positive constants, and ( v ) is the speed of the particle. The particle is moved to a distance ( b ) from the origin, and released with zero initial velocity. (a) What are the dimensions or SI units of ( V ) ? (b) What are the dimensions or SI units of ( P ) ? (c) Write Newton's second law for the object, in a form that involves only constants, ( v, x ), and derivatives involving only ( v ) and ( x ). (d) By direct integration from the previous equation, find ( x(v) ) for the particle. Note: Do not try to invert this to find ( v(x) ) ! Hint: you are not asked to find ( v(t) ) or ( x(t) ).$

Added by Chicken W.

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