KinematicsHard
Question
as a = - αu where α is a small constant. If the velocity of the particle is u0 at t = 0, then :-
Options
A.the particle will continue to move for a very long time
B.velocity of the particle will decrease by 50% in a time of 
C.the total distance covered by the particle will be 
D.all of the above
Solution
a = u.
= - αu
du = - α
dx
- u0 = - αx
or x =
(3rd option is correct)
Further,
= - αv or 
dt
log(u0) - log(0) = αt′
Since log (0) = - ∞
∴ t′ = ∞ (1st option is also correct)
Again, α
dt = - 
(Since 50% of u0 is 0/2)
αt″ =
αt″ = log 2
or t″ =
(2nd option is also correct)
= - αudu = - αdx- u0 = - αx
or x =
(3rd option is correct)Further,
= - αv or dtlog(u0) - log(0) = αt′
Since log (0) = - ∞
∴ t′ = ∞ (1st option is also correct)
Again, α
dt = - (Since 50% of u0 is 0/2)αt″ =
αt″ = log 2
or t″ =
(2nd option is also correct)Create a free account to view solution
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