21st sum

Asked by lovemaan5500 | 16th Dec, 2019, 09:35: PM

Expert Answer:

( dv/dt ) = - v  
 
dv/v = - dt
 
By integrating above eqn, we get,   ln(v) = -t + C  ..................(1)
 
where C is constant of integration.
 
At t = 0, we have v = 10, hence C = ln(10)
 
Hence eqn.(1) becomes,  ln(v/10) = -t   or    v = 10 e-t ...............(2)
 
velocity after 2 seconds,   v = 10 e-2 m/s
 
from eqn.(2), we get, v = dS/dt = 10 e-t ...................(3)
 
By integrating, S = -10 e-t + C  .....................(4)
 
where C is constant of integration
 
Let us assume, at t= 0, distance travelled with retrdation is zero
 
Hence using eqn.(4),  0 = -10 + C  or   C = 10
 
Hence eqn.(40 becomes,  S(t) = 10( 1 - e-t )
 
Hence ditance travelled after 2 seconds,  S = 10 ( 1 - e-2 ) m 

Answered by Thiyagarajan K | 17th Dec, 2019, 03:01: PM

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