Answer:
Explanation:
a )  V = 3 cos(0.5t)
differentiating with respect to t 
dv /dt = -3 x .5 sin0.5t
= -1.5 sin0.5t. 
acceleration = - 1.5 sin 0.5t
when t = 3 s 
acceleration = - 1.5 sin 1.5 
= - 1.496 ms⁻²
v = 3 cos.5t
b )  dx/dt = 3 cos 0.5 t
dx = 3 cos 0.5 t dt
integrating on both sides
x = 3 sin .5t / .5
x = 6 sin0.5t
At t = 2 s 
x = 6 sin 1
x = 5.05 m 
 
        
             
        
        
        
Answer:   Gases have three characteristic properties: (1) they are easy to compress, (2) they expand to fill their containers, and (3) they occupy far more space than the liquids or solids from which they form. An internal combustion engine provides a good example of the ease with which gases can be compressed.
Explanation:
 
        
             
        
        
        
Initially, the velocity vector is  . At the same height, the x-value of the vector will be the same, and the y-value will be opposite (assuming no air resistance). Assuming perfect reflection off the ground, the velocity vector is the same. After 0.2 seconds at 9.8 seconds, the y-value has decreased by
. At the same height, the x-value of the vector will be the same, and the y-value will be opposite (assuming no air resistance). Assuming perfect reflection off the ground, the velocity vector is the same. After 0.2 seconds at 9.8 seconds, the y-value has decreased by  , so the velocity is
, so the velocity is  .
.
Converting back to direction and magnitude, we get 
 
        
             
        
        
        
Explanation:
Given that,
Object-to-image distance d= 71 cm
Image distance = 26 cm
We need to calculate the object distance


We need to calculate the focal length
Using formula of lens

put the value into the formula



The focal length of the lens is 35.52.
(B). Given that,
Object distance = 95 cm
Focal length = 29 cm
We need to calculate the distance of the image
Using formula of lens

Put the value in to the formula




We need to calculate the magnification
Using formula of magnification



The magnification is 0.233.
The image is virtual.
Hence, This is the required solution.
 
        
             
        
        
        
9 because speed=distance/ time