CBSE Class 12-science Answered
21st sum
Asked by lovemaan5500 | 16 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 | 17 Dec, 2019, 03:01: PM
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