Question

A block is projected on a rough horizontal surface with static friction coefficient 0.5 and kinetic friction coefficient 0.4 .Its initial velocity is 8m/s .The total distance travelled by it till 3 sec is

Answer 1

Concept:

• friction opposes the relative motion between the surfaces involved.
• kinetic friction only acts during the motion and remains constant throughout.
• Static friction only acts whenever there is tendency of motion(or when object is at rest).

Solution:

Kinetic friction will act.

$\rm kinetic\: friction(f_k) = \mu_{k} mg$

$\implies\sf F_{net} = F_{driving} - F_{opposing}$

$\implies\sf ma = 0 - \mu_{k} mg$

$\implies\sf ma = - \mu_{k} mg$

$\implies\bf a = - \mu_{k} g =0.4(10) = 4 \: ms^{-2}$

★ Using equation of motion

--- s = ut +½at²

• initial velocity = u = 8 m/s
• time travelled = 3 s
• a = - 4 m/s²

$\to\sf s = 8(3) +\dfrac{1}{2}(-4)(3)^2$

$\to\sf s = 24 - 2(9) = 24 - 18$

$\to\bf s = 6\: m$

★★so,The total distance travelled by it till 3 sec is 6 m.