Derive the equation for the velocity addition for special...

Derive the equation for the velocity addition for special relativity. Show that: - Velocity does not exceed the value of c, irrespective of the velocity of the frame of reference or the object. - The velocity addition equation reduces to the Galilean transformation at velocities v << c.

Transcript

00:01 Hello everyone so let's start with the question so we have to derive the equation for the velocity addition for the space spatial relativity also we have to show that velocity does not exceed the value of c in respect to the velocity of frame of reference of object also the velocity addition equation reduced to gallian transformation at velocity so let's say there is two object that is c and b and here the frame of reference a and now the c is coming towards the a and b is coming towards a okay with respect to a so we can write that is vc b equal to vca minus v b b a divided by one minus vca multiply by v b a divided by c square and this formula is what this formula is the realistic formula of velocity addition okay this formula is realistic of velocity addition okay now here v ij represent what that velocity of i with respect to with respect to j now if these two particles p and c happens to travel at nearly the speed of light okay like means that the c and b they travel nearly the speed of land.

01:40 Okay, not exactly but you can consider as like near as possible.

01:48 Okay and so i can say that means the c is coming towards the a and b is coming towards the a means opposite of c with respect to a so you can say that the c and b faster with respect to each other means they are fast means they can see they are fast with respect to a and each other so i can say that that v c is approximate the speed of light and b b is approximate the speed of light so i can say that v c b equal to put the value of v that is here so i can say that c minus minus of c as the b is coming towards the c's in negative direction or you can say positive direction whatever the direction you can consider this as a negative direction divided by one minus c squared by c square that is minus so after solving this vc b we get that is 2c divided by c equal to divided by 2 and we get v c b c b equal to what c so here we have proved that that the equation for the velocity addition for the special relativity does not exit the value of c respect to the velocity of frame of reference okay so here the a is our frame of reference okay this a is our frame of reference and we can say that the velocity of both the c and b is not exceeding the c okay means it's you can say vcb is less than equal to c...

Question

Derive the equation for the velocity addition for special relativity. Show that: - Velocity does not exceed the value of c, irrespective of the velocity of the frame of reference or the object. - The velocity addition equation reduces to the Galilean transformation at velocities v << c.

Please give Ace some feedback