Question

Решите такую задачу СРОЧНО! __________________________ Автомобіль, рухаючись із постійним прискоренням, пройшов за 30с відстань 450 м і набув швидкість 18 м/c. Яка була його початкова швидкість?

Answer 1

Дано:
$v=$18 м/с
$S=450$ км
$t=30$ с
-------------------------------
$v_0-?$

оскільки прискорення постійне, то $a= \dfrac{v-v_0}{t}$. Шлях при рівноприскоренному : $S=v_0t+ \dfrac{at^2}{2}$

Підставивши $a=\dfrac{v-v_0}{t}$ в рівняння рівноприскоренного руху, маємо:

$S=v_0t+\dfrac{(v-v_0)t}{2} = \dfrac{2v_0t+vt-v_0t}{2} = \dfrac{(v_0+v)t}{2}$

звідси $v_0= \dfrac{2S}{t} -v= \dfrac{2\cdot450}{30} -18=12$ м/с

Відповідь: 12 м/с.

Answer 2

Problem Analysis

We are given the following information: - The car traveled a distance of 450 m in 30 seconds. - The car achieved a final velocity of 18 m/s.

We need to find the initial velocity of the car.

Solution

To solve this problem, we can use the following kinematic equation:

v = u + at

Where: - v is the final velocity - u is the initial velocity - a is the acceleration - t is the time

In this case, we know the final velocity (v = 18 m/s), the time (t = 30 s), and the distance (s = 450 m). We need to find the initial velocity (u).

To find the acceleration, we can use the formula:

s = ut + (1/2)at^2

Where: - s is the distance - u is the initial velocity - t is the time - a is the acceleration

Rearranging the equation, we get:

a = (2s - 2ut) / t^2

Substituting the given values, we can calculate the acceleration.

Once we have the acceleration, we can substitute it into the first equation to find the initial velocity.

Let's calculate the solution step by step.

Calculation

Given: - Distance (s) = 450 m - Time (t) = 30 s - Final velocity (v) = 18 m/s

Using the formula a = (2s - 2ut) / t^2, we can calculate the acceleration (a).

Substituting the given values: a = (2 * 450 - 2 * u * 30) / (30^2)

Simplifying the equation: a = (900 - 60u) / 900

Now, using the formula v = u + at, we can substitute the values of v, a, and t to find u.

Substituting the values: 18 = u + a * 30

Substituting the value of a: 18 = u + ((900 - 60u) / 900) * 30

Simplifying the equation: 18 = u + (900 - 60u) / 30

Multiplying both sides by 30: 540 = 30u + 900 - 60u

Combining like terms: 540 = -30u + 900

Rearranging the equation: 30u = 900 - 540

Simplifying: 30u = 360

Dividing both sides by 30: u = 12

Therefore, the initial velocity of the car was 12 m/s.

Answer

The initial velocity of the car was 12 m/s.