The question is a three part question. Part a) asked to find the average velocity with the equation $y= -\frac{1}{25}x^2 + \frac{4}{5}x$ on the interval $[6,10]$. Part b) asked to find the instantaneous velocity at $x=6$ and $x=10$. Part c) asks to find the acceleration at $x=4$. So I am not sure what to do after part b).
How do I find acceleration at $x=4$?
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calculus
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0It says to find the average velocity on that interval --- it doesn't say the function is defined only on that interval. – 2012-10-15
2 Answers
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Assuming that $y$ is meant to stand for a distance, and $x$ is meant to stand for time, then, as you probably know, instantaneous velocity is the rate of change of $y$ with respect to $x$. Acceleration is the rate of change of velocity with respect to $x$. So if you know what to do to $y$ to get the velocity, then you know what to do to the velocity to get the acceleration.
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Velocity is the instantaneous rate of change of position. Assuming $y(t)$ is position-time, we have
$V(x) = \frac{dy}{dx} = -\frac{2}{25}x+\frac{4}{5}$
and acceleration is the instantaneous rate of change of velocity:
$A(x) = \frac{dV}{dx} = -\frac{2}{25}$
Simply find now $A(4)$.