At any instant of time $t$, the displacement of any particle is given by $2 t-1$ (SI unit) under the

Question

At any instant of time $t$, the displacement of any particle is given by $2 t-1$ (SI unit) under the influence of force of 5 N . The value of instantaneous power is (in SI unit)

Professor PC Thomas Classes · Answer

(a) : Displacement of particle, $S=(2 t-1)$ SI unit Force, $F=5 \mathrm{~N}$ Instantaneous power is given by, $P=\frac{d W}{d t}$ where, $W$ is the work done on the particle. $ \begin{aligned} & P=\frac{d}{d t}(\vec{F} \cdot \vec{S})=F \cdot \frac{d S}{d t}=5 	imes \frac{d}{d t}(2 t-1)=5 	imes 2 \ & =10 	ext { SI Unit } \end{aligned} $