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Volgvan
3 years ago
6

You are driving at the speed of 27.7 m/s (61.9764 mph) when suddenly the car in front of you (previously traveling at the same s

peed) brakes and begins to slow down with the largest deceleration possible without skid- ding. Considering an average human reaction, you press your brakes 0.507 s later. You also brake and decelerate as rapidly as possible without skidding. Assume that the coefficient of static friction is 0.868 between both cars’ wheels and the road. The acceleration of gravity is 9.8 m/s2 . Calculate the acceleration of the car in front of you when it brakes. Answer in units of m/s2.
Physics
1 answer:
densk [106]3 years ago
4 0

Here when car in front of us applied brakes then it is slowing down due to frictional force on it

So here we can say that friction force on the car front of our car is given as

F_f = \mu m g

So the acceleration of car due to friction is given as

F_{net} = - \mu mg

a = \frac{F_{net}}{m}

a = -\mu g

now it is given that

\mu = 0.868

g = 9.81 m/s^2

so here we have

a = -0.868 * 9.81

a = -8.52 m/s^2

so the car will accelerate due to brakes by a = - 8.52 m/s^2

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Create the following matrix H:
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Answer:

a) {[1.25  1.5  1.75  2.5  2.75]

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Explanation:

Matrix H: {[1.25  1.5  1.75  2  2.25  2.5  2.75]

                [1  2  3  1  2  3  4]

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Its always important to get the dimensions of your matrix right. "Roman Columns" is the mental heuristic I use since a matrix is defined by its rows first and then its column such that a 2 X 5 matrix has 2 rows and 5 columns.

Next, it helps in the beginning to think of a matrix as a grid, labeling your rows  with letters (A, B, C, ...) and your columns with numbers (1, 2, 3, ...).

For question a, we just want to take the elements A1, A2, A3, A6 and A7 from matrix H and make that the first row of matrix G. And then we will take the elements B3, B4, B5, B6 and B7 from matrix H as our second row in matrix G.

For question b, we will be taking columns from matrix H and making them rows in our matrix K. The second column of H looks like this:

{[1.5]

[2]

[40]}

Transposing this column will make our first row of K look like this:

{[1.5  2  40]}

Repeating for columns 3, 5 and 7 will give us the final matrix K as seen above.

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