- #1

- 91

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x=2cos(at)

y=2sin(at)

prove particle moves in a circular path with constant angular velocity. prove that the acceleration of the particle at time t is in the direction of the radius from the particle to the centre of its path.

so i have

R=[2cos(at),2sin(at)]

V=[-2asin(at),2acos(at)]

A=[-2a^2cos(at),-2a^2sin(at)]

not sure how to show angular is constant.

i can take |V| and that s constant but im not using angular velocity.

for the second part:

if if i take direction of A= (d2y/dt2)/(d2x/dt2)=tan(at) where d2y/dt2 is second derivative of y wrt t

does this answer the question as motion is circle centre (o,0) so any radius will have tan (at) as its gradient?