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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 ) / 3β
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 ...
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!!!
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