A particle moves in a circle of radius 4. 0 cm clockwise at constant speed of 2 cms^(-1), Ifhat(x) and hat(y)are unit acceleration vectors along x-axis and y-axis respectively (in cms^(-2)) , find the acceleration of the particle at the instant half way between P and Q .

A particle moves in a circle of radius 4. 0 cm clockwise at constant s

1.	A particle moves in a circle of radius 4. 0 cm clockwise at constant speed of 2 cms^(-1), Ifhat(x) and hat(y)are unit acceleration vectors along x-axis and y-axis respectively (in cms^(-2)) , find the acceleration of the particle at the instant half way between P and Q .
Answer» Solution :As shown in the figure (ii) , let R be the midpoint of arc PQ . Then`ANGLE PQR = 45^(@)` Magnitude of accelerationat R , The acceleration a ACTS along RO Magnitude of component of along x-axis `a_(x) = a cos 45^(@)` `= 1 xx (1)/(sqrt(2)) = (1)/(sqrt(2)) CMS^(-2)` `:.hat (a) _(x)= - (1)/(sqrt(2)) x^(2)` Magnitude of component of a along y-axis, `a_(y) = 1 xx sin 45^(@)` `= (1)/(sqrt(2)) cms^(-2)` `:. hat(a)_(y) = - (1)/(sqrt(2)) hat(y)` Hence `hat(a) _(x) + hat(a)_(y) = (-1)/(sqrt(2)) (x^(2) + hat(y))`