Question

Velocity of a particle moving in a plane is given by v=2i m/s and its acceleration is given by a= -i + 2j m/s^2.Find the radius of curvature

Answer 1

Radius of curvature of a curve x(t) is given by
\[\rho = \left| \frac{ (1+ (\frac{ dx }{dt })^2)^{3/2} }{ \frac{ d^2x }{ dt^2}} \right|\]
Here |dx/dt |= |v |= 2 m/s
and |d^2 x/dt^2| =| a |= |-i+ 2j | m/s^2 = square root 5 m/s^2
Put the values and find the radius.

Answer 2

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