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
View Solution FreeMore Kinematics Questions
A particle moves in straight line in same direction for 20 seconds with velocity 3 m/s and then moves with velocity 4 m ...A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at 2 m/s2. He reaches ...A river is flowing east to west at a speed of 5 m / min. A on south bank of river, capable of swimming 10m/min in still ...A body starts from rest and is uniformly accelerated for 30 s. The distance traveled in the first 10 s is x1, next 10 is...A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height ...