A particle moves in a circle of radius ` 4.0 cm` clockwese at constant speed of ` 2cm S^(-1)` . If ` hat x` and ` hat y` ar unit accleration vectors along X- asis and Y-axis respectively, find the accleration of the particle at the instant half way between ` PQ. Fig. 2 ( d) . 38.
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Explanation

Let the particle be at ` R` , wher ` /_XOR= 45^@`. ltBrgt Magnitude of accelration at ®`
1 v^2 /r = (2 xx 2) /4 = 1 cm s^(-3)`
It is acting along ` RO` . Fig. 2 9d) . 44. ltbRgt :. Component of acceleration along X-axis,
` a-x =1 cos 45^@= 1// sqrt 2`
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So, ` vec a_x =- 1/ (sqrt2) hatx`
Component of acceleration along (Y) axis,
` a_y = 1 sin 45^@ = 1// sqrt2`
so, ` vec a_y =- 1/(sqrt 2) hat y`
:. ` vec A= vec _x = vec a_y =- (( hat x+ haty))/9 sqrt 2) cm s^(-2)`.