SOLUTION: Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x'(t) is its velocity, and x''(t) is its acceleration.
A particle moves along
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Question 1127316: Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x'(t) is its velocity, and x''(t) is its acceleration.
A particle moves along the x-axis at a velocity of v(t) = 3/(sqrt(t)), t > 0. At time t = 1, its position is x = 11. Find the acceleration and position functions for the particle.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ v(t))
\ +\ C\ =\ \int\,x'(t)\ =\ \int\,\frac{3}{\sqrt{t}}\ =\ 6\sqrt{t}\ +\ C)
But \ =\ 11)
so:
Hence
\ =\ 6\sqrt{t}\ +\ 5)
\ =\ v'(t)\ =\ \frac{d}{dt}\,\frac{3}{\sqrt{t}}\ =\ -\frac{3}{2t^{\small{\frac{3}{2}}})
John
My calculator said it, I believe it, that settles it
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