Thread: nstantaneous radius of curvature

An object is moving along an elliptical track and its x and y coordinates are recorded in meters by a stroboscope as follows:
x = ct

y = 1 - 2 c2 t2

with c=0.707 and t measured in seconds. What is the instantaneous radius of curvature at t = T?


T[s] = 0.96;

Could someone please show me how to solve it

For r(t) = x(t) i + y(t) j


k = |T '(t)|/ | r ' (t) |



Where T(t) = r ' (t)/ |r ' (t)|

The radius if curvature is then the reciprocal of the curvature p = 1/k