A block is projectd along a rough horizontal road with a speed of 10 m/s. If the coefficient of kinetic friction is 0.10 how far will it travel before coming to rest?

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Solution

Due to friction the body will decelerate. Let the deceleration be 'a'
$R - m g = 0 \Rightarrow R = m g$
Again $m a - μ R = 0 \Rightarrow m a = μ m g \Rightarrow a = μ g = 0.1 \times 10 = 1 m / s^{2}$
Initial velocity, u = 10 m/s
Final velocity, v = 0 m/s
$a = - 1 m / s^{2}$
$S = \frac{v^{2} - u^{2}}{2 a} = 0 - \frac{10^{2}}{2} (- 1) = \frac{100}{2} = 50 m$
It will travel 50 m before coming to rest.

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A block is projectd along a rough horizontal road with a speed of 10 m/s. If the coefficient of kinetic friction is 0.10 how far will it travel before coming to rest?

Due to friction the body will decelerate. Let the deceleration be 'a' R−mg=0⇒R=mg Again ma−μR=0⇒ma=μmg⇒a=μg=0.1×10=1m/s2 Initial velocity, u = 10 m/s Final velocity, v = 0 m/s a=−1m/s2 S=v2−u22a=0−1022(−1)=1002=50m It will travel 50 m before coming to rest.