Question

Автомобиль без начальной скорости начинает двигаться равноускоренно с ускорением "а". Через время t от начала движения скорость автомобиля перестает изменяться. Определить путь автомобиля, пройденый им за время 2t.

Answer 1

через время t скорость равна at, пройденый путь за это время

at^2/2, за оставшееся время t автомобиль пройдет at^2. общий путь

at^2+at^2/2=3/2(at^2)

 

Answer 2

Problem Analysis

We are given that a car starts moving with a constant acceleration "a" and after a time "t" its velocity stops changing. We need to determine the distance traveled by the car in a time of 2t.

Solution

To solve this problem, we can use the equations of motion for uniformly accelerated motion. The relevant equations are:

1. Final velocity (v) in terms of initial velocity (u), acceleration (a), and time (t): ``` v = u + at ``` where u is the initial velocity, a is the acceleration, and t is the time.

2. Distance (s) in terms of initial velocity (u), final velocity (v), acceleration (a), and time (t): ``` s = ut + (1/2)at^2 ``` where s is the distance traveled.

We are given that the car starts from rest, so the initial velocity (u) is 0. We are also given that the velocity stops changing after a time (t), so the final velocity (v) is also 0.

Using equation 1, we can find the time (t) when the velocity becomes 0: ``` 0 = 0 + at ``` Simplifying the equation, we find that t = 0 or a = 0. Since the car is moving with a constant acceleration, we can conclude that a ≠ 0. Therefore, t = 0 is not a valid solution.

Using equation 2, we can find the distance (s) traveled by the car in a time of t: ``` s = 0 * t + (1/2) * a * t^2 s = (1/2) * a * t^2 ```

To find the distance traveled by the car in a time of 2t, we substitute 2t for t in the equation: ``` s = (1/2) * a * (2t)^2 s = (1/2) * a * 4t^2 s = 2 * a * t^2 ```

Therefore, the distance traveled by the car in a time of 2t is 2 * a * t^2.

Answer

The distance traveled by the car in a time of 2t is 2 * a * t^2.

Explanation

When a car starts moving with a constant acceleration, its distance traveled can be calculated using the equation s = 2 * a * t^2.

Let's consider an example to illustrate this. Suppose the car starts moving with an acceleration of 5 m/s^2. After a time of t, the velocity of the car stops changing. To find the distance traveled by the car in a time of 2t, we can substitute the given values into the equation:

a = 5 m/s^2
t = 2 seconds

s = 2 * a * t^2
s = 2 * 5 * (2^2)
s = 2 * 5 * 4
s = 40 meters

Therefore, in this example, the car would travel a distance of 40 meters in a time of 2t.

Keep in mind that the actual values of acceleration and time may vary depending on the specific scenario.