Question

Два автомобиля выехали с автосанции через 3 минуты друг за другом и дигались с постоянным ускорением а=0.80м/с^2. через какой промежуток времени после начала движения второго автомобиля расстояние между ними станет s= 15км.?

Answer 1

Уравнение равноускоренного движения x = x0 + v0*t + a0*t^2 / 2.
Прими время старта второго авто за 0 (за точку отсчёта) и уравнение второго авто будет, очевидно,
x(2) = a*t^2 / 2
А первое авто уже ехало 3 минуты, его координата (x0) и скорость (v0) ненулевые, вычисли их и получишь уравнение движения первого авто.
Вычтя одно из другого, получишь окончательное уравнение (x1 - x2 = 15).

Answer 2

To solve this problem, we can use the equations of motion for uniformly accelerated motion. Let's break down the information given:

- The first car starts moving from the station. - After 3 minutes, the second car starts moving. - Both cars have a constant acceleration of a = 0.80 m/s^2. - We want to find the time it takes for the distance between the two cars to become s = 15 km.

Converting Units

First, let's convert the distance from kilometers to meters, as the acceleration is given in meters per second squared.

1 km = 1000 m

Therefore, s = 15 km = 15,000 m.

Calculating Time

To find the time it takes for the distance between the two cars to become 15,000 m, we can use the following equation:

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

Where: - s is the distance between the two cars (15,000 m) - u is the initial velocity (0 m/s, as both cars start from rest) - a is the acceleration (0.80 m/s^2) - t is the time we want to find

Rearranging the equation, we get:

t^2 + 2u/a * t - 2s/a = 0

Substituting the values, we have:

t^2 + 2(0)t - 2(15,000)/(0.80) = 0

Simplifying further:

t^2 - 37,500/0.80 = 0

t^2 - 46,875 = 0

Now, we can solve this quadratic equation to find the value of t.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Where: - a = 1 - b = 0 - c = -46,875

Substituting the values, we get:

t = (± √(0 - 4(1)(-46,875))) / (2(1))

t = (± √(0 + 187,500)) / 2

t = (± √(187,500)) / 2

t = (± 433.01) / 2

Since time cannot be negative, we take the positive value:

t = 433.01 / 2

t ≈ 216.51 seconds

Therefore, after approximately 216.51 seconds (or 3 minutes and 36.51 seconds) from the start of the second car's motion, the distance between the two cars will become 15 km.

Please note that this calculation assumes that the acceleration remains constant throughout the motion of both cars.

Answer 3

To solve this problem, we can use the equations of motion. Let's denote the initial velocity of the first car as v1 and the initial velocity of the second car as v2. We are given that both cars start from rest, so v1 = 0 and v2 = 0.

We are also given that both cars have a constant acceleration of a = 0.80 m/s^2. The time taken by the second car to reach a certain distance can be calculated using the equation:

s = v2*t + (1/2)*a*t^2,

where s is the distance, v2 is the initial velocity of the second car, t is the time, and a is the acceleration.

In this case, we want to find the time it takes for the distance between the two cars to become 15 km. Let's convert this distance to meters: 15 km = 15,000 m.

Substituting the given values into the equation, we have:

15,000 = 0*t + (1/2)*0.80*t^2.

Simplifying the equation, we get:

0.40*t^2 = 15,000.

Now, we can solve for t by rearranging the equation:

t^2 = 15,000 / 0.40.

t^2 = 37,500.

Taking the square root of both sides, we find:

t = sqrt(37,500).

Calculating the square root, we get:

t ≈ 193.65 seconds.

Therefore, after approximately 193.65 seconds (or about 3 minutes and 13.65 seconds) from the start of the second car's motion, the distance between the two cars will become 15 km.