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Karo-lina-s [1.5K]

2 years ago

15

A car is traveling at when the driver sees an accident m ahead and slams on the brakes. What constant deceleration is required t

o stop the car in time to avoid a pileup?

1 answer:

EleoNora [17]2 years ago

8 0

Answer:

Deceleration = $\frac{v^2}{2a}$ units/sec^2

Step-by-step explanation:

Given that a car is traveling at when the driver sees an accident m ahead and slams on the brakes.

i.e. if he is coming with speed v units/sec say, he has to make his velocity 0.

Distance travelled = m units

Initial velocity = v

Final velocity =0

Use the third formula as

$v^2=u^2+2as\\0=v^2+2am\\a =\frac{-v^2}{2a}$

So he has to apply an acceleration of $\frac{-v^2}{2a}$ units/sec^2 to stop the car in time to avoid a pile up.

Deceleration = $\frac{v^2}{2a}$ units/sec^2

You might be interested in

A set of five distinct positive integers has a mean of $1000$ and a median of $100$. What is the largest possible integer that c

mixer [17]

Answer:

e = 4796

Step-by-step explanation:

given,

mean of five distinct positive number = 1000

median of the number = 100

100 is median means two number will be less than 100 and two number will be greater than 100.

let five number be

a , b, c, d, e

'e' should be the largest number

As 100 is median so 'c' = 100.

'a' and 'b' should be as small as possible and d should be the number nearest to 100.

As all the number are distinct so the least number be equal to 1 and 2

now d will be equal to 101 (nearest to 100)

now,

sum of the five number = 5 x 1000 = 5000

a + b + c + d + e = 5000

1 + 2 + 100 + 101 + e = 5000

e = 5000 - 204

e = 4796

hence, the largest number will be equal to e = 4796

7 0

2 years ago

(x^(2)-11x+30)/(x^(2)-25)*(x^(2)+6x+5)/(x-5x-6) simplify the rational expression

DanielleElmas [232]

Simplify the following:
((x^2 - 11 x + 30) (x^2 + 6 x + 5))/((x^2 - 25) (x - 5 x - 6))

The factors of 5 that sum to 6 are 5 and 1. So, x^2 + 6 x + 5 = (x + 5) (x + 1):
((x + 5) (x + 1) (x^2 - 11 x + 30))/((x^2 - 25) (x - 5 x - 6))

The factors of 30 that sum to -11 are -5 and -6. So, x^2 - 11 x + 30 = (x - 5) (x - 6):
((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (x - 5 x - 6))

x - 5 x = -4 x:
((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (-4 x - 6))

Factor -2 out of -4 x - 6:
((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (2 x + 3) (x^2 - 25))

x^2 - 25 = x^2 - 5^2:
((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (x^2 - 5^2) (2 x + 3))

Factor the difference of two squares. x^2 - 5^2 = (x - 5) (x + 5):
((x - 5) (x - 6) (x + 5) (x + 1))/(-2(x - 5) (x + 5) (2 x + 3))

((x - 5) (x - 6) (x + 5) (x + 1))/((x - 5) (x + 5) (-2) (2 x + 3)) = ((x - 5) (x + 5))/((x - 5) (x + 5))×((x - 6) (x + 1))/(-2 (2 x + 3)) = ((x - 6) (x + 1))/(-2 (2 x + 3)):
((x - 6) (x + 1))/(-2 (2 x + 3))

Multiply numerator and denominator of ((x - 6) (x + 1))/(-2 (2 x + 3)) by -1:

Answer: (-(x - 6) (x + 1))/(2 (2 x + 3))

4 0

2 years ago

Gary has a 12gallon gas tank when he filled his tank up he pumped 8 gallons of gas what fraction of the tank had been empty

Assoli18 [71]

2/3 I believe is the answer

5 0

2 years ago

Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic f

vladimir2022 [97]

Answer:

Yes, I agree

Step-by-step explanation:

For the cubic function

A cubic function is represented as:

$f(x)=ax^3+bx^2+cx+d$

A cubic function may have 1, 2 or 3 x intercepts. This is shown below

For 3 x intercepts

$y = x^3 - x$

Equate y to 0

$x^3 - x = 0$

Expand

$x(x^2 - 1) = 0$

Express $x^2 - 1$ as difference of two squares

$x(x - 1)(x +1 ) = 0$

<em>x = 0 or 1 or -1</em>

For 2 x intercepts

$y = x^3 - x$

$y =(x-5)^2)(x+7)$

Equate y to 0

$(x-5)^2(x+7) = 0$

Expand

$(x-5)(x-5)(x+7) = 0$

<em>x= 5 or x = -7</em>

For 1 x intercept

$y = x^3$

Equate y to 0

$x^3 = 0$

Take cube roots of both sides

$x = 0$

It has been shown above that a cubic function may have 1, 2 or 3.

So, I agree to the statement

For the quadratic function

A quadratic function will not have any x intercept when the function can not be factorized;

E.g.

$y = x^2 + x + 17$

<em>The above function has no x intercept.</em>

A quadratic function will have at least 1 x intercept when the function can be factorized;

E.g.

$y = x^2- 6x + 9$

Equate y to 0

$x^2- 6x + 9 = 0$

Expand

$x^2 - 3x - 3x + 9 = 0$

$(x - 3)(x-3) = 0$

$x = 3$

We've shown that a quadratic may have no x intercept, and it may also have x intercept(s)

Hence, I agree to both statement

3 0

2 years ago

What is h(x) = 7 + 10x + x2 written in vertex form? h(x) = (x – 25)2 – 18 h(x) = (x – 5)2 + 32 h(x) = (x + 5)2 – 18 h(x) = (x +

muminat

Answer:c

Step-by-step explanation:

6 0

2 years ago