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An object is travelling in a horizontal ...

An object is travelling in a horizontal circle with uniform speed. At `t = 0, " the velocity is given by " vecu=20hati +35hatj km//s`. After one minute the velocity becomes `vecv= -20hati - 35hatj`. What is the magnitude of the acceleration?

Text Solution

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Magnitude of initial and final velocities =
`= u= sqrt((20)^2 + (35)^2) m//s`
`= sqrt1625 m//s`
`= 40.3 m//s`
As the velocity reverses in 1 min, the time period of revolution is 2 min.
`T=(2pi r)/u " giving " r = (uT)/(2pi)`
`a=u^2/r =(u^2 2pi)/(uT) = (2pi u)/T =(2xx3.14xx 40.3)/(2xx60) = 2.11 ms^(-2)`
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