A particle of unit mass is moving on a plane. Its trajectory,

A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by r(t) = t², θ(t), where f is time. The kinetic energy of the particle at time t = 2 is

r = t²
θ = t
x = r cos θ = t² cost
y = r sin θ = t² sint

u =	dx	= 2t cost - t² sint
	dt

at t = 2
u = 4 cos 2 – 4 sin 2 = – 5.301

v =	dy	= 2t sin t + t² cos t
	dt

at t = 2
v = 4 sin 2 + 4 cos 2 = 1.972
V = √u² + v² = 5.656

K.E. =	1	= mv²
	2

=	1	= × 1 × 5.656² = 15.99
	2