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# M2-kinematics of a partic watch

1. A particke moves along the xaxis such that its displacement x metres from the origin O at time t seconds is given by

x=2+t-(1/10)e^t

Find correct to 1dp the value of t when the velocity of P is zero.

Okay i need to do dx/dt obv, but can't do that with e^t, do i ln everything like...

lnx=ln2+lnt-ln1/10xe^t (and then differentiate)

and i don't think u can ln like this can you??? when you ln both sides it should be lnx=ln(2+t....)

Or maybe i differentiate e^t sepperately...

ARGG help!
2. d/dt{e^t} = e^t

i.e. dx/dt = 1 - e^t /10
A particke moves along the xaxis such that its displacement x metres from the origin O at time t seconds is given by

x=2+t-(1/10)e^t

Find correct to 1dp the value of t when the velocity of P is zero.

Okay i need to do dx/dt obv, but can't do that with e^t, do i ln everything like...

lnx=ln2+lnt-ln1/10xe^t (and then differentiate)

and i don't think u can ln like this can you??? when you ln both sides it should be lnx=ln(2+t....)

Or maybe i differentiate e^t sepperately...

ARGG help!
dx/dt = 1 - (1/10)e^t

dx/dt = 0: 1 - (1/10)e^t = 0

(1/10)e^t = 1

e^t = 10

t = ln 10 = 2.3 s
4. (Original post by elpaw)
d/dt{e^t} = e^t

i.e. dx/dt = 1 - e^t /10
oh god....."e's are easy" i am so stupid!!!
(thank you!)
5. just wondering now though...if you have a question like

3=e^t+ A

you do ln3=ln(e^t +A) ?
or erm ln(3-A)=tlne
ie ln (3-A)=t

so you can't do ln3=lne^t+lnA right?

my brains seem to be turning into mushy peas....
so you can't do ln3=lne^t+lnA right?
no, you cant do that.
you do ln3=ln(e^t +A) ?
or erm ln(3-A)=tlne
ie ln (3-A)=t
both are correct
7. (Original post by elpaw)
no, you cant do that.

both are correct
gotcha thanks!

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