Question

A particle moves along a straight line with displacement ( s(t) ), velocity ( v(t) ), and acceleration ( a(t) ). Show that [ a(t)=v(t) frac{d v}{d s} ] Explain the difference between the meanings of the derivatives ( d v / d t ) and ( d v / d s ). Answer ( downarrow ) ( d v / d t ) is the rate of change of velocity with respect to time; ( d v / d s ) is the rate of change of velocity with respect to displacement

          A particle moves along a straight line with displacement ( s(t) ), velocity ( v(t) ), and acceleration ( a(t) ).
Show that
[
a(t)=v(t) frac{d v}{d s}
]
Explain the difference between the meanings of the derivatives ( d v / d t ) and ( d v / d s ).
Answer ( downarrow )
( d v / d t ) is the rate of change of velocity with respect to time; ( d v / d s ) is the rate of change of velocity with respect to displacement

$A particle moves along a straight line with displacement ( s(t) ), velocity ( v(t) ), and acceleration ( a(t) ). Show that [ a(t)=v(t) fracd vd s ] Explain the difference between the meanings of the derivatives ( d v / d t ) and ( d v / d s ). Answer ( downarrow ) ( d v / d t ) is the rate of change of velocity with respect to time; ( d v / d s ) is the rate of change of velocity with respect to displacement$

Added by Steve A.

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