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| PAGE: 117 | SET: Exercises | PROBLEM: 107 |
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 
.
(a)
Calculate linear model of reaction time distance.
Observe the table.
Excel sheet method is used to find the linear regression equation.
Observe the graph:
The linear regression model of the data for reaction time distance is 
.
(b)
Calculate quadratic model of Braking time distance.
Observe the table.
Excel sheet method is used to find the quadratic regression equation.
Observe the graph:
The quadratic regression model of the data for braking time distance is 
.
(c)
The total stopping distance is equal to reaction time distance plus braking time reaction .
Stopping distance of the car 
.
(d)
Graph:
Draw the coordinate plane.
Plot the Reaction time distance function 
.
Plot the Braking time distance function 
.
Plot the Stopping time distance function 
.
(e)
Find the derivative of 
.
The Stopping time distance function .
Apply derivative on each side with respect to .
(i)
Find the rate of change of total stopping time at 
.
Substitute 
in the derivative of the total stopping distance.
.
Rate of change of total stopping time at is 
.
(ii)
Find the rate of change of total stopping time at 
.
Substitute 
in the derivative of the total stopping distance.
.
Rate of change of total stopping time at is 
.
(iii)
Find the rate of change of total stopping time at 
.
Substitute 
in the derivative of the total stopping distance.
.
Rate of change of total stopping time at is 
.
(f)
Observe the results obtained in (e).
Rate of change of total stopping time at is 
.
Rate of change of total stopping time at is 
.
Rate of change of total stopping time at is 
.
As speed increases, the rate of change in total stopping time increases.
(a) The linear regression model for reaction time distance is .
(b) The quadratic regression model for braking time distance is .
(c) Graph of the , and 
is
(d)
Rate of change of total stopping time at is .
Rate of change of total stopping time at is .
Rate of change of total stopping time at is .
(f) As speed increases, the rate of change in total stopping time increases.
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