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Formula for calculating centripetal acceleration can be derived as follows.

Fig. 1

X and Y are the two points in the circular path where the velocities are ‘v

as shown above is ‘r’. ‘dr’ is the change in positions. Consider here the motion is uniform i.e. velocities are

constant. From the definition of acceleration we can write a = (v

It appears that the above expression will result zero. But, due to different direction the expression 1 will result

some value. We can write equation 1 as

a = dv/dt ------- (2)

Representing the velocity vectors by vector diagram we get.

Where

ω is the angular velocity and r is the radius of the circle. Centripetal acceleration in terms of angular velocity is written as

a

Placing the values in the above equation

a

a

a

v = 25 m/s

Radius of the turn is half of the diameter value given in the question.

r = d/2

r = 6/2

r = 3m

Placing the values in equation 1

a

a