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A man moves on his motorbike with 54km/h and the take u turn (180deg) and continues to move withsame speed .The time of u turn is 10s Find Average acceleration during u turn !

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Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
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The centripetal force when turning in a circle at constant speed is given by:

F = m*(v2/r)

Where v is the speed (54 km/h) and r is the radius of the circle.  Since Force = mass* acceleration, the average acceleration (a) during the turn is:

a = v2/r

We know v = 54 km/h, but we need to find r, the radius of turn.  The man turns 180 degrees, which is 1/2 of a circle.  The circumference of a circle is 2*pi*r.  The man travels half a circumference at 54 km/hr in 10 seconds.  Hence:

54*(10/3600) = pi*r                                           [10/3600 converts 10 sec into hours]

(0.15)/(3.14) = r ≅ 0.048 km

Hence a = (54)2/(0.048) = 61,072.6 km/hr2 = 4.71 m/s2 = 0.48 g's  (where 1 g = 9.8 m/s2).