$\"\"$

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The stopping distance of the car moving with a speed $\"\"$ is equal to distance traveled by the car during reaction time $\"\"$ plus distance traveled by the car after applying brakes $\"\"$ .

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(a)

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Calculate linear model of reaction time distance.

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Observe the table.

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Excel sheet method is used to find the linear regression equation.

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$\"\"$

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Observe the graph:

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The linear regression model of the data for reaction time distance is $\"\"$ .

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$\"\"$

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(b)

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Calculate quadratic model of Braking time distance.

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Observe the table.

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Excel sheet method is used to find the quadratic regression equation.

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$\"\"$

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Observe the graph:

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The quadratic regression model of the data for braking time distance is $\"\"$ .

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$\"\"$

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(c)

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The total stopping distance is equal to reaction time distance $\"\"$ plus braking time reaction $\"\"$ .

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$\"\"$

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Stopping distance of the car $\"\"$ .

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$\"\"$

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(d)

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Graph:

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Draw the coordinate plane.

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Plot the Reaction time distance function $\"\"$ .

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Plot the Braking time distance function $\"\"$ .

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Plot the Stopping time distance function $\"\"$ .

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$\"\"$

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$\"\"$

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(e)

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Find the derivative of $\"\"$ .

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The Stopping time distance function $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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(i)

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Find the rate of change of total stopping time at $\"\"$ .

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Substitute $\"\"$ in the derivative of the total stopping distance.

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$\"\"$ .

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Rate of change of total stopping time at $\"\"$ is $\"\"$ .

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(ii)

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Find the rate of change of total stopping time at $\"\"$ .

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Substitute $\"\"$ in the derivative of the total stopping distance.

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$\"\"$ .

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Rate of change of total stopping time at $\"\"$ is $\"\"$ .

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(iii)

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Find the rate of change of total stopping time at $\"\"$ .

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Substitute $\"\"$ in the derivative of the total stopping distance.

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$\"\"$ .

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Rate of change of total stopping time at $\"\"$ is $\"\"$ .

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$\"\"$

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(f)

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Observe the results obtained in (e).

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Rate of change of total stopping time at $\"\"$ is $\"\"$ .

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Rate of change of total stopping time at $\"\"$ is $\"\"$ .

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Rate of change of total stopping time at $\"\"$ is $\"\"$ .

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As speed increases, the rate of change in total stopping time increases.

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$\"\"$

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(a) The linear regression model for reaction time distance is $\"\"$ .

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(b) The quadratic regression model for braking time distance is $\"\"$ .

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(c) Graph of the $\"\"$ , $\"\"$ and $\"\"$ is

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$\"\"$

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(d)

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Rate of change of total stopping time at $\"\"$ is $\"\"$ .

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Rate of change of total stopping time at $\"\"$ is $\"\"$ .

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Rate of change of total stopping time at $\"\"$ is $\"\"$ .

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(f) As speed increases, the rate of change in total stopping time increases.