Question

Поезд начал двигаться равноускоренно с ускорением 2 м/с² и за 10 с проехал некоторый путь. Найти скорость поезда в средней точке пути?

Answer 1

V=v0+at; V0=0; V=at; V=10*2=20м/с

Answer 2

$s =\frac{at^2}{2} \\ s/2 = \frac{at_0^2}{2} \\t_0=t/\sqrt 2\\v_0=at_0=at/\sqrt2=2*10/\sqrt2=14.14$

Answer 3

Problem Analysis

We are given that a train starts moving with a constant acceleration of 2 m/s² and travels for 10 seconds to cover a certain distance. We need to find the speed of the train at the midpoint of its journey.

Solution

To find the speed of the train at the midpoint of its journey, we can use the equations of motion. The equation that relates distance, initial velocity, time, and acceleration is:

s = ut + (1/2)at²

where: - s is the distance traveled, - u is the initial velocity, - t is the time, and - a is the acceleration.

In this case, we know the acceleration (a = 2 m/s²), the time (t = 10 s), and we need to find the distance traveled (s).

To find the distance traveled, we can rearrange the equation as follows:

s = (1/2)at²

Substituting the known values, we have:

s = (1/2)(2 m/s²)(10 s)²

Simplifying, we get:

s = 100 m

So, the train travels a distance of 100 meters in 10 seconds.

To find the speed of the train at the midpoint of its journey, we can use the equation:

v = u + at

where: - v is the final velocity (speed), - u is the initial velocity, - a is the acceleration, and - t is the time.

In this case, we know the initial velocity (u = 0 m/s), the acceleration (a = 2 m/s²), and the time (t = 10 s).

Substituting the known values, we have:

v = 0 m/s + (2 m/s²)(10 s)

Simplifying, we get:

v = 20 m/s

Therefore, the speed of the train at the midpoint of its journey is 20 m/s.

Answer

The speed of the train at the midpoint of its journey is 20 m/s.