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a particle moves with a decreasing speed along the circle of radius r so that at any moment its tang and centripetal acc are equal in magnitude.at t=0,its speed is u.plz time after which speed reduce to 0

a particle moves with a decreasing speed along the circle of radius r so that at any moment its tang and centripetal acc are equal in magnitude.at t=0,its speed is u.plz time after which speed reduce to 0

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear jauneet

at any instant tangential acceleraion is given by = dV/dt

but this is equal to centripital acceleation which is given as = mV2/r

  so   dV/dt = V2/r

        dV/V2 = 1/r dt

    ∫dV/V2 =∫ 1/r dt

    -1/V = 1t/r + C

 apply condition at t=0 V=u

 so C=-1/c

equation become   -1/V = 1t/r + -1/u

                            1/V = 1/u  + t/r

                             1/V =(r+tu)/ur

                            V=ur/(r+tu)

                       so clearly after infinite time particle will come to rest

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Badiuddin

                           

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