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A body moves in straight line under the retardation a which is given by a= bv² if the initial velocity is 2 m/s the distance covered in time t=2 second

A body moves in straight line under the retardation a which is given by a= bv² if the initial velocity is 2 m/s the distance covered in time t=2 second
 

Grade:11

1 Answers

Ravneet
104 Points
5 years ago
 Retarding acceleration = -bv2. (We are assuming that b is a constant and v represents velocity here)
                                                 ( - ) shows retarding acceleration
 
Now,  acceleration = dv/dt
 
Hence, dv/dt = -bv2     
 
dv/v2 = -bdt --------------------------------------on rearranging 
 
Integrating from t = 0, v = u to t = t and v =v       here   u is initial velocity
                                                                                      
 
[1/u-1/v] = -bt
 
1/v = 1/u+ bt
 
1/v = (1+ubt)/u                                   solve for v
 
v = u/(1+ubt)
 
Now v = dx/dt                    because we have to find displacement
                           
dx/dt = u/(1+ubt)
 
dx = u/(1+ubt). dt
 
Integrating from x = 0, t = 0 to x = x, t = t
 
x = u/ub * ln|1+ubt| 
 
x = ln|1+ubt|/b 
 
And now put t=2 sec and u = 2m/s
 
x = ln|1+4b|/b 

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