Question

Suppose Swarglok (heaven) is in constant motion at a speed of $0.9999 \mathrm{c}$ with respect to the earth. According to the earth's frame, how much time passes on the earth before one day passes on Swarglok?

Answer 1

Hint: We should know that velocity is defined as the rate change of displacement per unit time. Speed in a specific direction is also known as velocity. Velocity is equal to displacement divided by time. Speed, being a scalar quantity, is the rate at which an object covers distance. The average speed is the distance which is a scalar quantity per time ratio. On the other hand, velocity is a vector quantity; it is direction-aware. An object which moves in the negative direction has a negative velocity. If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion in this case. Based on this we have to solve this question.

Complete step by step answer
We know that the word displacement implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object. Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude. It is represented as an arrow that points from the starting position to the final position. For Example- If an object moves from A position to B, then the object's position changes. Displacement is defined as the act of moving someone or something from one position to another or the measurement of the volume replaced by something else. An example of displacement is when war requires people to move from their homes due to the danger.
It is given that: $\quad \mathrm{v}=0.9999 \mathrm{c}$
Time elapsed on Swarglok $\tau=1$ day
$\therefore$ Time passed on earth $\quad \mathrm{t}=\dfrac{\tau}{\sqrt{1-(\mathrm{v} / \mathrm{c})^{2}}}$

$\therefore \mathrm{t}=\dfrac{1}{\sqrt{1-(0.9999)^{2}}}=70.7 \mathrm{days}$

Note:We should know that if an object's speed or velocity is increasing at a constant rate then we say it has uniform acceleration. The rate of acceleration is constant. If a car speeds up then slows down then speeds up it doesn't have uniform acceleration. The instantaneous acceleration, or simply acceleration, is defined as the limit of the average acceleration when the interval of time considered approaches 0. It is also defined in a similar manner as the derivative of velocity with respect to time. If an object begins acceleration from rest or a standstill, its initial time is 0. If we get a negative value for acceleration, it means the object is slowing down. The acceleration of an object is its change in velocity over an increment of time. This can mean a change in the object's speed or direction. Average acceleration is the change of velocity over a period of time. Constant or uniform acceleration is when the velocity changes the same amount in every equal time period.