Question

A block is projected with speed $20m/s$ on a rough horizontal surface. The coefficient of friction $\left(\mu \right)$ between the surfaces varies with time $\left(t\right)$ as shown in figure. The speed of body at the end of $4$ second will be $(g=10m/s^2)$.

• A. $2m/s$
• B. $5m/s$
• C. $7.2m/s$
• D. $9.5m/s$

Answer 1

The correct option is A $2m/s$

From 0 to 2 sec;

frictional force $={\mu }_{1}mg=0.5m\times 10=5m$

deacceleration,

$a_1=\frac{5m}{m}=5m/s^2$

Distance travelled by block in $25s$;

$x_1=20t-\frac{1}{2}{a}_1{t}^2=20\times 2-\frac{1}{2}\times 5\times 2^2=40-10=30m$

Speed of block after $2s$;

$v-u=-at=20-5\times 2=10m/s$

After $2s$ to $4s$,

frictional force, $f_2={\mu }_{2}mg=0.4\times 10m=4m$

${\mu }_2=$ average from $0.5$ to $0.4s$

deacceleration,

$a_2=\frac{4m}{m}=4m/s^2$

Now, new velocity after $2s$ is

$v^{\prime }-10=-4\times t$

$\Rightarrow v^{\prime }=10-8=2m/s$