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3.1, #10, Given Problem.
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3.1, #10, Given Problem. |
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We use the Power Rule, which means we multiply the entire quantity by the exponent, and reduce the exponent by 1. |
3.1, #42, Given Problem.
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3.1, #42, Given Problem. |
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Part (a).
We know that the velocity is the first derivative of the distance formula. We also know that the accelation is the first derivative of the velocity formula, and the second derivative of the distance formula. |
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Part (b).
We use our accelaration formula from part (a), and substitute 1 second for t. The -2 indicates that the particle is decelerating by 2 m/s/s after 1 second. |
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Part (c).
Here we have the distance formula, velocity formula, and acceleration formula plotted on the same set of axes. |
3.1, #60, Given Problem.
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3.1, #60, Given Problem. |
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We use our derivative rules to differentiate the generic function. We used the power rule, the constant multiple rule and the difference rule. |
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Here we use the given information about the first derivative of 1 and the first derivative of (-1) to get two different equations in a and b. |
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We take our two equations from the last step and solve them simultaneously using the method of addition. |
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Knowing a and b, we can go back to the original function. C is now our only missing quantity. We now also make use of the given fact that f(2)=15 to make a substitution and solve for c. |
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Now we have the complete equation for the parabola that was asked for. |
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