Question

A small body of mass $m$ is located on a horizontal plane at the point $O$. The body acquires a horizontal velocity $v_0$. Find the mean power developed by the friction force during the whole time of motion, if the friction coefficient $k=0.27$, $m=1.0kg$, and $v_0=1.5m/s$.

• A. $-4W$
• B. $4W$
• C. $-3W$
• D. $2W$

Answer 1

The correct option is D $2W$

Frictional force acting $f=kmg$

Acceleration of the body $a=\frac{f}{m}=kg$

$⟹$ $a=0.27\times 10=2.7m/s^2$

Final velocity of the body $v_o=1.5m/s$

Initial velocity of the body $u=0m/s$

Using $v_o=u+at$

Or $1.5=0+\left(2.7\right)t$

$⟹$ $t=0.56$ s

Work done $W=\Delta K.E=\frac{1}{2}m{v}_o^2-\frac{1}{2}m{u}^2$

Or $W=\frac{1}{2}\left(1\right)(1.5{)}^2-0=1.125J$

Thus mean power $P=\frac{W}{t}=\frac{1.125}{0.56}$

$⟹$ $P=2W$