Question

When a particle is thrown in mud pond, it looses half of its speed after penetrating 3cm into mud. How much further it will penetrate before coming to rest ?(Assume that mud po nd offers uniform retardation)

Answer 1

Let the initial velocity of the body be u. Its velocity becomes u/2 after penetrating 3 cm in the mud . We can calculate the deceleration of the body using these.
v²= u² +2as
u²/4 = u² + 2a×3
-3u²/4 = 6a
a = -u²/8

Now, we can calculate the distance the body travels till it comes to rest.

v² = u² + 2as
0 = u² +2×(-u²/8)×s
u² = u²s/4
s = 4 cm

Therefore, the body penetrates 1 cm (4-3=1cm) more before coming to rest.

Hope this helps :)