How much weight will a Machine working at the power of 100 W, be able to lift at a constant speed of 1m/s vertically? (Take$\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2$)

Given, 

Power of the Machine P = 100 W,

Speed of lifting v = 1m/s

g = 10m/s²

We know, Power is given as, P = $\frac{\mathrm{W}}{\mathrm{t}}$……(i)

where W is work done and t is time.

Now, work done is given as, W = F x d ……(ii)

where F is force and d is displacement.

Putting (ii) in (i), we get

P = $\frac{\mathrm{F}\times \mathrm{d}}{\mathrm{t}}$

P = F x v       [ where v = $\frac{\mathrm{d}}{\mathrm{t}}$]
⇒$\mathrm{F}=\frac{\mathrm{P}}{\mathrm{v}}$
⇒$\mathrm{F}=\frac{100}{1}$
⇒F = 100N
Also, F = ma
⇒ $\mathrm{m}=\frac{\mathrm{F}}{\mathrm{a}}$
⇒$\mathrm{m}=\frac{100}{10}$ 

$\Rightarrow \mathrm{m}=10 \mathrm{kg}$
Therefore, the person is able to lift 10 kg at the speed of 1m/s.