Question

The stopping distance of an automobile, on dry, level pavement, traveling at a speed v (in kilometers per hour) is the distance R (in meters) the car travels during the reaction time of the driver plus the distance B (in meters) the car travels after the brakes are applied (see figure). The table shows the results of the experiment. (Round your coefficients to 3 decimal places.) Reaction time Braking distance R Driver sees obstacle Driver applies brakes B Car stops Speed, v 20 40 60 80 100 Reaction Time 7.6 16.0 24.3 32.6 41.0 Distance, R Braking Time 1.6 8.3 19.5 35.1 55.2 Distance, B (a) Use the regression capabilities of a graphing utility to find a linear model for the reaction time distance R. (Round numerical values to four decimal places.) R(v) = (b) Use the regression capabilities of a graphing utility to find a quadratic model for braking distance B. (Round numerical values to four decimal places.) B(v) = (c) Determine the polynomial giving the total stopping distance T. (Round numerical values to four decimal places.) T(v) =

          The stopping distance of an automobile, on dry, level pavement, traveling at a speed v (in kilometers per hour) is the distance R (in meters) the car travels during the reaction time of the driver plus the distance B (in meters) the car travels after the brakes are applied (see figure). The table shows the results of the experiment. (Round your coefficients to 3 decimal places.)
Reaction
time
Braking
distance
R
Driver sees
obstacle
Driver applies
brakes
B
Car
stops
Speed, v
20 40 60 80 100
Reaction Time
7.6 16.0 24.3 32.6 41.0
Distance, R
Braking Time
1.6 8.3 19.5 35.1 55.2
Distance, B
(a) Use the regression capabilities of a graphing utility to find a linear model for the reaction time distance R. (Round numerical values to four decimal places.)
R(v) =
(b) Use the regression capabilities of a graphing utility to find a quadratic model for braking distance B. (Round numerical values to four decimal places.)
B(v) =
(c) Determine the polynomial giving the total stopping distance T. (Round numerical values to four decimal places.)
T(v) =

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The stopping distance of an automobile, on dry, level pavement, traveling at a speed v (in kilometers per hour) is the distance R (in meters) the car travels during the reaction time of the driver plus the distance B (in meters) the car travels after the brakes are applied (see figure). The table shows the results of the experiment. (Round your coefficients to 3 decimal places.)
Reaction
time
Braking
distance
R
Driver sees
obstacle
Driver applies
brakes
B
Car
stops
Speed, v
20 40 60 80 100
Reaction Time
7.6 16.0 24.3 32.6 41.0
Distance, R
Braking Time
1.6 8.3 19.5 35.1 55.2
Distance, B
(a) Use the regression capabilities of a graphing utility to find a linear model for the reaction time distance R. (Round numerical values to four decimal places.)
R(v) =
(b) Use the regression capabilities of a graphing utility to find a quadratic model for braking distance B. (Round numerical values to four decimal places.)
B(v) =
(c) Determine the polynomial giving the total stopping distance T. (Round numerical values to four decimal places.)
T(v) =

Added by Alexander B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert William Semus

10/05/2022

Step 1

The data points are as follows: Speed (v): 20, 40, 60, 80, 100 Reaction Time Distance (r): 7.6, 16, 24.3, 32.6, 41 Performing linear regression on this data gives us the equation: \[ R(v) = 0.417v - 0.72 \] ** Show more…

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The stopping distance of an automobile, on dry, level pavement, traveling at a speed v (in kilometers per hour) is the distance R (in meters) the car travels during the reaction time of the driver plus the distance B (in meters) the car travels after the brakes are applied (see figure). The table shows the results of the experiment. (Round your coefficients to 3 decimal places.) Reaction time Braking distance Driver sees obstacle Driver applies brakes Car stops Speed, v 20 40 60 80 100 Reaction Time Distance, R 7.6 16.0 24.3 32.6 41.0 Braking Time Distance, B 1.6 8.3 19.5 35.1 55.2 (a) Use the regression capabilities of a graphing utility to find a linear model for the reaction time distance R. (Round numerical values to four decimal places.) R(v) = (b) Use the regression capabilities of a graphing utility to find a quadratic model for braking distance B. (Round numerical values to four decimal places.) B(v) = (c) Determine the polynomial giving the total stopping distance T. (Round numerical values to four decimal places.) T(v) =

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00:01 So in this question, they say that the stopping distance of an automobile on dry level pavement, traveling at a speed v in kilometers per hour, is the distance are in meters that the car travels during the reaction time of the driver, plus the distance b in meters that the car travels after the brakes are applied see the figure.

00:22 The table shows the results of the experiment, and we will round our coefficients to three decimal places.

00:28 In part a, they say, i want to use the regrettable.

00:31 Capabilities of a graphing utility to find a linear model for the reaction time distance r.

00:39 So i'm going to head to my calculator and i'm going to go into my stat and i'm going to edit.

00:47 I'm going to clear out what i have in l1 and l2.

00:55 Now in l1 i'm going to put my x values, which are my speeds this time.

01:01 They're 20, 40.

01:05 60, 80, and 100.

01:11 And in l2, i'm going to put my values of r.

01:14 So 7 .6, 16, 24 .3, 32 .6, and 41.

01:28 Once i've done so, i'm going to go to stat again, and i'm going to calculate a linear regression on the data set that's in l1 and l2.

01:38 I calculate, and what am i getting? i'm getting .417x minus .72.

01:47 So here i'm getting, i'm going to use v instead of x, but i'm getting 0 .417v, and then this was plus b, which is negative 0 .72, so minus 0 .72.

02:04 In part b, use the regression capabilities of a graphing utility to find a quadratic model for the breaking distance b, again rounding our numerical values to four decimal places.

02:18 So i'm going back to my calculator, and now i'm going to say going back to stat, i'm going to edit, and in l2, i'm going to have 1 .6, i'm going to have 8 .3, 19 .5, 35 .1 .1.

02:37 And 55 .2.

02:43 And what do i do? i'm going to quit.

02:45 I'm going to stat calculate a quadratic regression on l1 and l2...

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