Answer:
B- The amount of matter in a certain
amount of space
Explanation:
Density is the amount of matter an object has in a certain space. To find density, divide the mass of an object by the volume of an object.
 
        
                    
             
        
        
        
Answer:
v_max = (1/6)e^-1 a
Explanation:
You have the following equation for the instantaneous speed of a particle:
 (1)
   (1)
To find the expression for the maximum speed in terms of the acceleration "a", you first derivative v(t) respect to time t:
![\frac{dv(t)}{dt}=\frac{d}{dt}[ate^{-6t}]=a[(1)e^{-6t}+t(e^{-6t}(-6))]](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%28t%29%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Bate%5E%7B-6t%7D%5D%3Da%5B%281%29e%5E%7B-6t%7D%2Bt%28e%5E%7B-6t%7D%28-6%29%29%5D) (2)
  (2)
where you have use the derivative of a product.
Next, you equal the expression (2) to zero in order to calculate t:
![a[(1)e^{-6t}-6te^{-6t}]=0\\\\1-6t=0\\\\t=\frac{1}{6}](https://tex.z-dn.net/?f=a%5B%281%29e%5E%7B-6t%7D-6te%5E%7B-6t%7D%5D%3D0%5C%5C%5C%5C1-6t%3D0%5C%5C%5C%5Ct%3D%5Cfrac%7B1%7D%7B6%7D)
For t = 1/6 you obtain the maximum speed.
Then, you replace that value of t in the expression (1):

hence, the maximum speed is v_max = ((1/6)e^-1)a
 
        
             
        
        
        
Answer:
0.37 m
Explanation:
The angular frequency, ω, of a loaded spring is related to the period, T,  by

The maximum velocity of the oscillation occurs at the equilibrium point and is given by

A is the amplitude or maximum displacement from the equilibrium.

From the the question, T = 0.58 and A = 25 cm = 0.25 m. Taking π as 3.142,

To determine the height we reached, we consider the beginning of the vertical motion as the equilibrium point with velocity, v. Since it is against gravity, acceleration of gravity is negative. At maximum height, the final velocity is 0 m/s. We use the equation

 is the final velocity,
 is the final velocity,  is the initial velocity (same as v above), a is acceleration of gravity and h is the height.
 is the initial velocity (same as v above), a is acceleration of gravity and h is the height.


 
        
             
        
        
        
Answer:
Force on the proton will be 
Explanation:
We have given speed of proton is 20.3% of speed of light
Speed of light 
So speed of proton 
Magnetic field B = 0.00629 T
Charge on proton 
Angle between velocity and magnetic field 
Force on the proton is equal to 
 
        
             
        
        
        
<span>superconductors, conductors, semiconductors, insulators </span>