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# How is the power related to the speed at which a body can be lifted? How many kilograms will a man working at the power of $100\ W$, be able to lift at constant speed of $1\ m s^{-1}$ vertically? $(g=10\ ms^{-2})$

**Relation between power and speed:**

Power, $P=\frac{work\ done}{time}$

$=\frac{mgh}{t}$ [$m\rightarrow mass,\ h\rightarrow height,\ t\rightarrow time,\ g\rightarrow gravity$]

$=mg\frac{h}{t}$

$=mgv$ [$\frac{h}{t}=speed(v)$]

As given, Power $P=100\ W$

Gravitational acceleration $g=10\ ms^{-2}$

Speed at which the object to be uplifted $v=1\ ms^{-1}$

Let $m$ be the mass of the object. We have to find $m=?$

On using $P=mgv$

$100=m\times10\times1$

Or $10m=100$

Or $m=\frac{100}{10}\ kg$

Or $m=10\ kg$

Therefore, the man can be able to lift $10\ kg$ mass at the given speed.

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