differential equation- last one!!

ok i actualy hate these bloomin questions
a sculler is rowing a two kilometer course she starts rowing at 5m/s but gradualy tires so that when she has rowed x meters her speed it

5e^-0.0001x m/s how long will she take to finish the course?

my working

dx/dt= 5e^-0.0001x

dt/dx= 1/(5e^-0.0001x)=1/5 e^-0.0001x

t=intergral dt/dx= intergral 1/5 e^-0.0001x = -2000 e^-0.0001x+c

given initial t=o when x=0 c=2000

so when x=2000
t= -2000e^-.2 +2000 =362 sec

which is wrong. where have i gone wrong? thanks soooo much

Reply 1

El Stevo

11

a sculler is rowing a two kilometer course she starts rowing at 5m/s but gradualy tires so that when she has rowed x meters her speed it

5e^-0.0001x m/s how long will she take to finish the course?

dx/dt = 5e^-0.0001x

Int e^0.0001x dx = Int 5 dt

10000e^0.0001x = 5t + c

t = 2000e^0.0001x + k

k=0 as x=0 when t=0

t = 2000e^0.0001x
when x=2000
t = 2000e^0.2
t = 2442.8s

Reply 2

BCHL85

12

I don't see anywhere wrong (I can't check the last calculation)

Reply 3

BCHL85

12

ah right
The integration with "-" sign . Sorry :biggrin:

Reply 4

sarah12345

OP

2

El Stevo

a sculler is rowing a two kilometer course she starts rowing at 5m/s but gradualy tires so that when she has rowed x meters her speed it

5e^-0.0001x m/s how long will she take to finish the course?

dx/dt = 5e^-0.0001x

Int e^0.0001x dx = Int 5 dt

10000e^0.0001x = 5t + c

t = 2000e^0.0001x + k

k=0 as x=0 when t=0

t = 2000e^0.0001x
when x=2000
t = 2000e^0.2
t = 2442.8s

the answers 443s

Reply 5