Can the magnitude of an object’s displacement be larger than the distance it has traveled?
What is the condition for them being equal? Explain.
This is my first week learning physics, so I have only a rudimentary knowledge. Thanks for your help.
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displacement is the magnitude of the vector from the initial position (usually taken to be the origin, in which case it is the standard radial vector r) to final position. distance traveled is the length you would measure if you took the path it traveled, and stretched it out into a straight line and measured it, or the distance your cars odometer would read if you took that trip.
mathematically:
the dispalcement is the magnitude of the radial vector
if r is the position vector at any time t, the distance traveled is the arc length of the curve represented parametrically by r(t), or the integral(r'*r')^1/2 where r' is the derivative with respect to t and * is the inner product
they are equal only when the curve traveled is a straight line AND it starts from the origin