Question

1) Движение точки происходит по закону S(t) = -4t² + 7t - 2. В какой момент времени скорость движения равна 6?2) Движение точки происходит по закону S(t) = -5t² + 2t - 1. В какой момент времени скорость движения равна 4?

Answer 1

1 Скорость движения - это первая производная от пути. Найдем производную, приравняем ее к 6 и получим время.
v (t) = s '(t)= - 8 t +7;   v(t) = 6;

 - 8t + 7 = 6;
- 8t = -1;
t = 1/8;
t= 0,125,
2)  s '(t) = - 10 t +2;   v (t)= 4;
 -10 t + 2 = 4;
 -10 t = 2;
проверьте условие во втором номере, время не может быть отрицательным , а по вашему условию получается минус 0,2

Answer 2

I will try to answer your questions in detail.

1) The movement of a point occurs according to the law S(t) = -4t² + 7t - 2. At what time is the speed of movement equal to 6?

To find the time when the speed of movement is equal to 6, we need to find the derivative of the function S(t), which is the velocity function V(t). The derivative of a function is the rate of change of the function with respect to the variable. The derivative of a polynomial function is obtained by multiplying each term by the power of the variable and then subtracting one from the power. For example, the derivative of 3x² is 6x. Using this rule, we can find the derivative of S(t):

V(t) = S'(t) = -4(2t) + 7(1) - 0 = -8t + 7

Now, we need to find the value of t that makes V(t) equal to 6. We can do this by setting V(t) equal to 6 and solving for t:

V(t) = 6 -8t + 7 = 6 -8t = -1 t = 1/8

Therefore, the speed of movement is equal to 6 at the time t = 1/8.

2) The movement of a point occurs according to the law S(t) = -5t² + 2t - 1. At what time is the speed of movement equal to 4?

Similarly, we need to find the derivative of the function S(t), which is the velocity function V(t):

V(t) = S'(t) = -5(2t) + 2(1) - 0 = -10t + 2

Then, we need to find the value of t that makes V(t) equal to 4:

V(t) = 4 -10t + 2 = 4 -10t = 2 t = -1/5

Therefore, the speed of movement is equal to 4 at the time t = -1/5.

I hope this helps you understand the problem. If you need more help, you can use the tool [Mathway](https://www.mathway.com/ru/Algebra), which can solve algebra problems step by step. You can also read more about the [law of motion](https://ru.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%B4%D0%B2%D0%B8%D0%B6%D0%B5%D0%BD%D0%B8%D1%8F) and the [equation of motion of a point](https://obrazovaka.ru/fizika/uravnenie-dvizheniya-tochki.html) on Wikipedia.