Question

Show that P= F vector . V vector

Answer 1

We know that,

• Work done by a body is equal to the dot product of force exerted and displacement produced.

In Equation form, the relation is given as,

• $\bold\green{W=\vec{F}.\vec{s}}$

where,

$W = Work \:done$

$\vec{F }= Force \:vector$

$\vec{s }= displacement\:vector$

Now,

Dividing both the sides wrt time ( t ),

We get,

$=>\frac{W}{t}=\frac{\vec{F}.\vec{s}}{t}\\\\=>\frac{W}{t}=\vec{F}.\frac{\vec{s}}{t}$

But,

we know that,

$\frac{W}{t}=P\quad and \quad \frac{\vec{s}}{t}=\vec{v}$

Therefore,

Putting the values,

We get,

$\bold\red{P=\vec{F}.\vec{v}}$

where,

$P = Power$

$\vec{F }= Force \:vector$

$\vec{v }= velocity\: vector$

Thus,

• Power consumption of a body is given by the dot product of force exerted and velocity acquired by the body.

• The SI unit of Power is Joule , denoted by symbol J.

• $\bold{1 J = 1\:Nm{s}{-1}}$

Answer 2

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