Answer:
The maximum length during the motion is 
Explanation:
From the question we are told that 
            The mass  is  
             The vertical spring  length is  
             The unstretched  length is  
           The initial speed is 
           The new length of the spring 
The spring constant k is mathematically represented as 
                            
 
Where F is the force applied  
            y is the difference in weight which is   
The negative sign is because the displacement of the spring (i.e its extension occurs against the force F)
     Now  substituting values accordingly 
                     
                        
The  elastic potential energy is given as 
   where D is this the is the displacement  
Since Energy is conserved the total elastic potential energy would be
              
              
 
Substituting value accordingly 
                 
                 
                  
                 
So to obtain total length we would add the unstretched length 
  So we have 
                   
                                
                 
                
                   
                      
 
        
                    
             
        
        
        
Because the box keeps going straight at the same speed, while the seat under it speeds up, slows down, or changes direction.
        
             
        
        
        
Answer:
A) The space time coordinate x of the collision in Earth's reference frame is 
 .
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B) The space time coordinate t of the collision in Earth's reference frame is 

Explanation:
We are told a rocket travels in the x-direction at speed v=0,70 c (c=299792458 m/s is the exact value of the speed of light) with respect to the Earth. A collision between two comets is observed from the rocket and it is determined that the space time coordinates of the collision are (x',t') = (3.4 x 10¹⁰ m, 190 s). 
An event indicates something that occurs at a given location in space and time, in this case the event is the collision between the two comets. We know the space time coordinates of the collision seen from the reference frame of the rocket and we want to find out the space time coordinates in Earth's reference frame.
<em>Lorentz transformation</em>
The Lorentz transformation relates things between two reference frames when one of them is moving with constant velocity with respect to the other. In this case the two reference frames are the Earth and the rocket that is moving with speed v=0,70 c in the x axis.
The Lorentz transformation is 
                           
                                 
                                 
                           
prime coordinates are the ones from the rocket reference frame and unprimed variables are from the Earth's reference frame. Since we want position x and time t in the Earth's frame we need the inverse Lorentz transformation. This can be obtained by replacing v by -v and swapping primed an unprimed variables in the first set of equations
                        
                            
                            
                         
First we calculate the expression in the denominator
                             
                                 
then we calculate t
                       
                       
                       
                       
finally we get that 
                                      
then we calculate x
                          
                          
                          
                          
                          
                          
finally we get that 
                                      
 
        
             
        
        
        
Hope this helps :)
When describing linear motion, you need only one graph representing each of the three terms, while projectile motion requires a graph of the x and y axes. Graphs of simple harmonic motion are sine curves. Circular motion is different from other forms of motion because the speed of the object is constant.
        
             
        
        
        
Weight. Because there is less gravity on the moon.