Question

Скорость автомобиля, движущегося с ускорением 4м/с2 на участке длинной 81м увеличилась в 3 раза. Чему была равна скорость автомобиля в начале участка? Напишите пожалуйста полное решение.

Answer 1

Ответ:

9 м/с

Объяснение:

См.фото

Answer 2

Problem Analysis

We are given the following information: - The car is moving with an acceleration of 4 m/s^2. - The length of the segment is 81 m. - The speed of the car at the end of the segment is 3 times its initial speed.

We need to find the initial speed of the car.

Solution

Let's assume the initial speed of the car is v m/s.

Using the equation of motion, we can find the final speed of the car at the end of the segment: v_final = v + a * t

Here, a is the acceleration (4 m/s^2) and t is the time taken to cover the segment.

To find the time taken, we can use the equation: s = v * t + (1/2) * a * t^2

Here, s is the distance covered (81 m).

Simplifying the equation, we get: (1/2) * a * t^2 + v * t - s = 0

This is a quadratic equation in t. We can solve it using the quadratic formula: t = (-b ± sqrt(b^2 - 4ac)) / (2a)

In this case, a = (1/2) * a, b = v, and c = -s.

Let's calculate the time taken using the quadratic formula.

Calculation

Substituting the values into the quadratic formula: t = (-v ± sqrt(v^2 - 4 * (1/2) * a * (-s))) / (2 * (1/2) * a)

Simplifying further: t = (-v ± sqrt(v^2 + 2 * a * s)) / a

Now, we have two possible values for t. We need to select the positive value since time cannot be negative.

Let's calculate the time taken using the positive value of t.

Calculation Continued

Substituting the values into the equation: t = (-v + sqrt(v^2 + 2 * a * s)) / a

Now, we can substitute the value of t into the equation for final speed to find the final speed of the car.

Calculation Continued

Substituting the values into the equation: v_final = v + a * t

Simplifying further: v_final = v + a * ((-v + sqrt(v^2 + 2 * a * s)) / a)

Simplifying further: v_final = v - v + sqrt(v^2 + 2 * a * s)

Simplifying further: v_final = sqrt(v^2 + 2 * a * s)

We are given that the final speed of the car is 3 times its initial speed: v_final = 3 * v

Substituting this into the equation: 3 * v = sqrt(v^2 + 2 * a * s)

Squaring both sides of the equation: 9 * v^2 = v^2 + 2 * a * s

Simplifying further: 8 * v^2 = 2 * a * s

Substituting the given values: 8 * v^2 = 2 * 4 * 81

Simplifying further: 8 * v^2 = 648

Dividing both sides of the equation by 8: v^2 = 81

Taking the square root of both sides of the equation: v = 9 m/s

Answer

The initial speed of the car was 9 m/s.