91影视

(a)

Using Galileo鈥檚 velocity addition rule, write the equation for the velocity of a particle with respect to S.

$u=\stackrel{炉}{u}+v$

Here, v is the velocity of the frame$\stackrel{炉}{s}$ with respect to S, u is the speed of a particle with respect to S, and $\stackrel{炉}{u}$is the velocity of a particle with respect to $\stackrel{炉}{S}$.

From the above equation, as u and v are constants, the velocity of a particle with respect to$\stackrel{炉}{S}$$\left(\stackrel{炉}{u}\right)$will also be constants. Hence,

$\stackrel{炉}{u}=u-v$

Hence, Newton鈥檚 law is valid in the frame$\stackrel{炉}{S}$.

Therefore, the frame$\stackrel{炉}{S}$is also an inertial frame.

(b)

When the frame is an inertial frame, the velocity of the particle in the frame $\stackrel{炉}{S}$will be constant.

Rearrange the equation role="math" localid="1656069585995" $\stackrel{炉}{u}=u-v$in terms of v.

$v=u-\stackrel{炉}{u}$

As the velocity of a particle with respect todata-custom-editor="chemistry" $\stackrel{炉}{\mathrm{S}}$is constant, the values of u and $\stackrel{炉}{u}$will also be constant.

Therefore, the frame$\stackrel{炉}{S}$ moves with uniform velocity with respect to frame S.