Question

В формуле пути s=20t-2t в квадрате Укажите начальную скорость и определите ускорение Сколько времени оно движется? Какой путь оно пройдет?

Answer 1

$S= v_{0}t+ \frac{a t^{2} }{2}$

$v_{0}=20$

$a=4$

из формулы не возможно определить время (т.к. это уравнение), а путь будет разным для разного времени (зависимость S(t))

Answer 2

Problem Analysis

We are given the formula for distance traveled as a function of time: s = 20t - 2t^2. We need to determine the initial velocity, acceleration, time of motion, and the distance traveled.

Initial Velocity

The initial velocity can be determined by finding the derivative of the distance function with respect to time and evaluating it at t = 0. Let's find the derivative of s with respect to t:

s'(t) = 20 - 4t.

To find the initial velocity, we substitute t = 0 into the derivative:

v(0) = 20 - 4(0) = 20.

Therefore, the initial velocity is 20.

Acceleration

The acceleration can be determined by finding the derivative of the velocity function with respect to time. Let's find the derivative of v with respect to t:

v'(t) = -4.

Therefore, the acceleration is -4.

Time of Motion

To find the time of motion, we need to solve the equation s = 20t - 2t^2 for t. Let's set s equal to zero and solve for t:

20t - 2t^2 = 0.

Factoring out t, we get:

t(20 - 2t) = 0.

This equation is satisfied when either t = 0 or 20 - 2t = 0. Solving the second equation for t, we get:

20 - 2t = 0.

2t = 20.

t = 10.

Therefore, the time of motion is 10.

Distance Traveled

To find the distance traveled, we substitute t = 10 into the distance function:

s(10) = 20(10) - 2(10)^2 = 200 - 200 = 0.

Therefore, the distance traveled is 0.

Summary

Based on the given formula s = 20t - 2t^2: - The initial velocity is 20. - The acceleration is -4. - The time of motion is 10. - The distance traveled is 0.

Please let me know if I can help you with anything else.