Question

A block of mass $10\text{kg}$ is moving with a uniform speed of $20\text{m/s}$ enters onto a rough surface of coefficient of friction $0.8$, the time taken by the block to come to rest is

• A. $2.5\text{s}$
• B. $5\text{s}$
• C. $7.5\text{s}$
• D. $10\text{s}$

Answer 1

The correct option is A $2.5\text{s}$

Given, mass of the block $\left(m\right)=10\text{kg}$
speed $\left(u\right)=20\frac{m}{s}$
when the block comes to rest final velocity $\left(v\right)=0$



From $FBD$:
$R=mg=10g=100\text{N}$
Here, friction acts as retarding force
$f=-ma=\mu R$
$f=0.8\times 100=80\text{N}(\because f=\mu R$
$\Rightarrow a=\frac{80}{10}=-8\frac{m}{s^2}$

Applying kinematic relation $v=u+at$
$\Rightarrow 0=u+at$
$t=\frac{u}{(-a)}=\frac{20}{8}=2.5\text{s}$