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Sanchit Gupta Grade: 12
        

A particle having velocity V = V0 at t = 0 is decelerated at the rate |a| = β √V , where β is a positive constant. Choose the correct option(s) :-


(a) The particle comes to rest at t = (2 √V0 ) / β


(b) The particle will come to rest at infinty


(c) The distance travelled by the particle is (2 V0 3/2  ) / β


(d) The distance travelled by the particle is (2 V0 3/2  ) /

6 years ago

Answers : (2)

vikas askiitian expert
510 Points
										

a = k(v)1/2


a = dv/dt = -dv/dt in case of retardation


 


-dv/dt = k(v)1/2


 v-1/2dv = -kdt


 [2v1/2] lim from u to v    = -k[t]   lim from 0 to t


 2v1/2 - 2u1/2 = -kt


 u = vo (given) so


 2v1/2 - 2vo1/2 = -kt       ..............1


particle comes to rest when final velocity becomes 0 ,


from eq 1 , put v = 0


    t = 2vo1/2/k                        (option a)


now use v =  dx/dt


 find a relation in bw x & time ,then put t = 2vo1/2 /k u will get the result ...

6 years ago
Aarthi Sundaram
10 Points
										

you have initial velocity u= v0


final velocity, v=0


a= beta/rootV


use v=u+at


you'll get option (a) on isolating t.


simple!!!

6 years ago
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