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A body moving with uniform retardation covers 3km before its speed is reduced to half of its initial value. It comes to rest in another distance of? i) 1km ii) 2km iii) 3km iv) 1/2 km Please show the steps.
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A body moving with uniform retardation covers 3km before its speed is ...
Solution:

Given, initial velocity u = u, final velocity v = u/2, distance covered s1 = 3 km.

We know that,

v^2 – u^2 = 2as

where a is the retardation and s is the distance covered.

Applying the formula for the distance covered before reaching half the initial speed,

v^2 – u^2 = 2as1

(u/2)^2 – u^2 = 2a(3)

u^2/4 – u^2 = 6a

3u^2 = 24a

a = 3u^2/24

a = u^2/8

Now, we can find the distance covered before the body comes to rest.

Let this distance be s2.

We know that,

v^2 – u^2 = 2as

0 – (u/2)^2 = 2a(s1 + s2)

u^2/4 = 2(u^2/8)(s1 + s2)

s1 + s2 = 1/2 km

Therefore, the body comes to rest in another distance of 1/2 km.

Answer: (iv) 1/2 km
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A body moving with uniform retardation covers 3km before its speed is ...
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A body moving with uniform retardation covers 3km before its speed is reduced to half of its initial value. It comes to rest in another distance of? i) 1km ii) 2km iii) 3km iv) 1/2 km Please show the steps.
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