Question

Тело двигается с места в течении 10 секунд, с ускорением 3 м/с2. Какое время понадобится, чтобы преодолеть последний метр пути? народ помогите заранье благодарен

Answer 1

$x(t) = at^2/2 = 1.5t^2\\ 1.5*10^2-1.5*t^2 = 1\\ t^2 = 99\frac{1}{3}\\ t = \sqrt{99\frac{1}{3}}\\ \Delta t = 10-t = 0.033$

Answer 2

Problem Analysis

We are given the following information: - The body is moving from rest for a duration of 10 seconds. - The acceleration of the body is 3 m/s^2. - We need to find the time it takes to cover the last meter of the distance.

Solution

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

\[distance = initial\ velocity \times time + \frac{1}{2} \times acceleration \times time^2\]

In this case, the initial velocity is 0 m/s because the body starts from rest. The distance is 1 meter, and the acceleration is 3 m/s^2. We need to find the time it takes to cover this distance.

Substituting the given values into the equation, we have:

\[1 = 0 \times t + \frac{1}{2} \times 3 \times t^2\]

Simplifying the equation, we get:

\[1 = \frac{3}{2} \times t^2\]

To solve for time, we can rearrange the equation:

\[t^2 = \frac{2}{3}\]

Taking the square root of both sides, we get:

\[t = \sqrt{\frac{2}{3}}\]

Calculating the value, we find:

\[t \approx 0.816\] seconds

Therefore, it will take approximately 0.816 seconds to cover the last meter of the distance.

Answer

The time it will take to cover the last meter of the distance is approximately 0.816 seconds.