[填空题]
1.Car $A$ and Car $B$ are travelling in the same direction along a straight line. In the reference frame of a stationary observer on the ground, Car $A$ has a speed of $24ms^-1$ and Car B has a speed of $36ms^-1$.
1.Explain what is meant by a frame of reference.
2.Calculate the velocity of Car $B$ relative to the stationary observer in Car $A$. $u'$ = $ms^-1$
3.The distance travelled by Car $B$ relative to Car $A$ is $60m$ in a time interval of $5.0s$. Calculate the distance travelled by Car $B$ relative to the stationary observer on the ground for the same time interval. $Δx$ = $m$
2.Now consider two spaceships, $C$ and $D$, traveling through space towards a planet.
Both of the spaceships turn on their lights. The turning on of the lights of spaceship $C$ and the turning of the lights of spaceship $D$ are defined as Events $C$ and $D$ respectively. Event C has coordinates $x_C=3.456\times10^{5} $,$t_C=0s$ and event $D$ has coordinates $x_D=3.443\times10^{5}$, $t_D=1.1\times10^{-3}s$ according to a stationary observer on the planet.
A rocket flies towards the two spaceships at a speed of $0.85c$ according to the same observer.
1.According to the frame of reference of the rocket, determine the space differences between events $C$ and $D$. $Δx′$ = $\times10^{-5}\,m$
2.According to the frame of reference of the rocket, determine the space-time interval between events $C$ and $D$. $(Δs′)^2$ = $\times10^{11}\,m^2$
3.Discuss whether Event $C$ and Event $D$ can occur at the same time according to some other inertial frame. $(Δs)^2$ =
