The x and y coordinates of a particle moving in a plane are given by x(t)=a (p t) and y(t)=b (p t) where a, b( a) and p are positive constants of appropriate dimensions and t is time. Then, which of the following is not true?

Step-by-step solution

aligned & x=a (p t), y=b (p t) & x^2 a^2 + y^2 b^2 =1, i.e. equation of ellipse & Now, r=x i + j =a (p t) i +b (p t j & v= d r d t =-p asin (p t) i +p b (p t) j & a= d v d t =-p^2 a (p t) i -p^2 b (p t) j & at t= 2 p & v=-p a i and a =-p^2 b j aligned v perpendicular to a Also, a=-p^2 r , i.e. directed towards a fixed point