IIT JEE , AIEEE Forum - Physics , Mechanics

armaan

A particle moves in a straight line with vel. given by dx/dt=x+1.(x is the distance described) .Time taken by particle to transverse a distance of 99 mts is ?

akhil_o

dx/(x+1)=dt

integrating

_{[ 0]}

^{[ 99]} dx/(x+1) =_{[ 0]}

^{[ t]} dt

ln(x+1)|₀⁹⁹=t-0

ln(100)-ln(1)=t
ln(100)=t

ln (x+1)=t

x=99

t=ln 100 seconds

edit

elastiboysai

dx/x+1=dt
ln(x+1)=t+c
initial condition needs to be given to get the exact equation.
x+1=e^t *e^c
u want dist only..
so assume at t=0,x=0 so c=0
_{[0 ]}

^{[99 ]} x+1=_{[0 ]}

^{[t ]}e^t
x^2/2+x=e^t-1
now plug in
4999.5=e^t-1
t=ln5000.5
edited

hash_include

elasti, youve made a mstake..
when t = 0, x = 0.. so c = 0.. not 1

elastiboysai

ya sorry
careless typing
neway das wat i meant

armaan

ln5000 is that ur answer elasti ?

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