The velocity of a certain particle is moving along the x axis is proportional to x. At time t=0 the particle is located at x=2 and at time t=10 it is at x=4. Find the position at t=5?
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11
Answer:
From the question we get to know that the velocity v is proportional to x.
Hence, v=kx where k is any constant and v=dx/dt.
So, dx/dt = kx.
Now, if we integrate on both sides we will get.
Or, ln x = kt + c (since integration of dx/x is lnx).
From the question we have at t=0 , x=2.
And at t=10 , x=4 .
So at t=5 , x will be.
ln 2 = c(at time t=0 and x=2) .
ln 4 = 10k + c (at time t=10 and x=4).
ln x = 5k + c.
Thus, on solving the above equation we will get x=8^1/2.
Answered by
2
Answer:
8 power 12 or root 8
Explanation:
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