Question

A block is projected 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?

Answer 1

Friction force acting on the block will decelerate it.
Let the deceleration be 'a'.
Using free body diagram

R − mg = 0
(where R is the normal reaction force)
⇒ R = mg                 (1)
Again, ma − μ_kR = 0
(where μ_k is the coefficient of kinetic friction)
From Equation (1),
⇒ ma = μ_kmg
⇒ a = μ_kg = 0.1 × 10
      = 1 m/s²
Given:
initial velocity, u = 10 m/s
final velocity, v = 0 m/s (block comes to rest)
                       a = −1 m/s² (deceleration)
Using equation of motion v² - u² = 2as
(where s is the distance travelled before coming to rest)
`s=(v^2-u^2)/(2a)`
On substituting the respective values, we get

`=0-10^2/2(-1)`

`=100/2=50"m"`

Therefore, the block will travel 50 m before coming to rest.