The instantaneous power in terms of force F and instantaneous velocity v is

Question

The instantaneous power in terms of force F and instantaneous velocity v is (A) P=F ⋅ t (B) P=F ⋅ v (C) P=F ⋅ v-1 (D) P=F ⋅ v-2

Tardigrade Admin · Accepted Answer

Instantaneous power, P= displaystyle lim Δ t arrow 0 ( text Work done / text Time taken ) =|(d W/d t)| As, d W=F ⋅ d r ⇒ P=F ⋅ (d r/d t) Again, (d r/d t)=v, instantaneous velocity Therefore, P=F ⋅ v=F v cos θ

Q. The instantaneous power in terms of force $F$ and instantaneous velocity $v$ is

$P = F \cdot t$

$P = F \cdot v$

$P = F \cdot v^{- 1}$

$P = F \cdot v^{- 2}$

$P = F \cdot v \cdot t^{- 1}$

Instantaneous power, $P = Δ t \to 0 lim \frac{Work done}{Time taken}$
$= ∣ ∣ \frac{d W}{d t} ∣ ∣$
As,
$d W = F \cdot d r$
$\Rightarrow P = F \cdot \frac{d r}{d t}$
Again, $\frac{d r}{d t} = v$ , instantaneous velocity
Therefore, $P = F \cdot v = F v cos θ$

Q. The instantaneous power in terms of force F and instantaneous velocity v is

P=F⋅t

P=F⋅v

P=F⋅v−1

P=F⋅v−2

P=F⋅v⋅t−1

Instantaneous power, P=Δt→0lim​ Time taken Work done ​ =∣∣​dtdW​∣∣​ As, dW=F⋅dr ⇒P=F⋅dtdr​ Again, dtdr​=v, instantaneous velocity Therefore, P=F⋅v=Fvcosθ