Question

Поезд движется с начальной скоростью v0=36км/ч с ускорением а=0.2 м/с^2. Через сколько времени его скорость увеличится вдвое и какой путь он пройдет за это время

Answer 1

36 км/ч - это 10 м/с. Считаем, за сколько времени скорость увеличится вдвое:
$v=v_0+at\\20=10+0,2t\\t=50(s)$

Пройденный путь:
$s=v_0t+\frac{at^2}{2}=10*50+\frac{0,2*50^2}{2}=750(m)$

Ответ: 50 секунд; 750 метров.

Answer 2

Дано: V₀=36км/ч=10м/с, V=2V₀, a=0,2м/с²,
Найти: t, S
V=2V₀=2*10=20м/с,
a=(V-V₀)/t⇒ t=(V-V₀)/a,
время t=(20-10)/0,2=10/0,2=50c
путь S
1способ. S=V₀t+at²/2, S= 10*50+0,2*50²/2=750 м
2 способ. S=(V+V₀)t/2, S= (20+10)*50/2= 750 м

Answer 3

Problem Analysis

We are given the initial velocity of a train, v0 = 36 km/h, and the acceleration, a = 0.2 m/s^2. We need to find the time it takes for the train's velocity to double and the distance it travels during that time.

Solution

To solve this problem, we can use the equations of motion. The equation that relates velocity, acceleration, and time is:

v = v0 + at,

where: - v is the final velocity, - v0 is the initial velocity, - a is the acceleration, and - t is the time.

We are given that the train's velocity doubles, so the final velocity, v, will be 2 times the initial velocity, v0.

v = 2v0.

Substituting this into the equation of motion, we have:

2v0 = v0 + at.

Simplifying the equation, we get:

t = (2v0 - v0) / a.

Now we can calculate the time it takes for the train's velocity to double.

To find the distance traveled during this time, we can use the equation of motion that relates distance, initial velocity, acceleration, and time:

d = v0t + (1/2)at^2.

Substituting the values we know, we have:

d = v0 * [(2v0 - v0) / a] + (1/2) * a * [(2v0 - v0) / a]^2.

Simplifying the equation, we get:

d = v0^2 / a.

Now we can calculate the distance traveled by the train during the time it takes for its velocity to double.

Calculation

Substituting the given values into the equations:

- v0 = 36 km/h = 10 m/s, - a = 0.2 m/s^2.

We can now calculate the time and distance:

t = (2 * 10 - 10) / 0.2 = 10 / 0.2 = 50 seconds.

d = (10^2) / 0.2 = 100 / 0.2 = 500 meters.

Therefore, it will take the train 50 seconds to double its velocity, and it will travel a distance of 500 meters during that time.

Answer

The train will take 50 seconds to double its velocity, and it will travel a distance of 500 meters during that time.