Question

Помогите пожалуйста срочно! Тело массой m движется прямолинейно по закону s(t) =at^2+bt+c,где a, b, c постоянные величины. Докажите что сила действующая на это тело постоянна. ​

Answer 1

Ответ:

Объяснение:

F=ma, где а - ускорение

скорость v=S'=2at+b

ускорение a=v'=2a

F=m*2a

F=2am, поскольку ускорение не зависит от времени и масса тоже не зависит от времени, то сила, которая действует на тело - постоянная

Answer 2

Proof that the force acting on the body is constant

To prove that the force acting on the body is constant, we need to analyze the motion of the body described by the equation s(t) = at^2 + bt + c, where a, b, and c are constants.

The force acting on an object is given by Newton's second law of motion, which states that force (F) is equal to the mass (m) of the object multiplied by its acceleration (a). In this case, we need to find the acceleration of the body.

The acceleration can be obtained by taking the second derivative of the position function s(t) with respect to time (t). Let's calculate it step by step:

1. First, let's differentiate s(t) with respect to time (t) to find the velocity function v(t): ``` v(t) = ds(t)/dt = d(at^2 + bt + c)/dt = 2at + b ```

2. Next, let's differentiate v(t) with respect to time (t) to find the acceleration function a(t): ``` a(t) = dv(t)/dt = d(2at + b)/dt = 2a ```

From the above calculation, we can see that the acceleration (a) is a constant value of 2a. Therefore, the force acting on the body is constant, as it is proportional to the acceleration.

In conclusion, the force acting on the body described by the equation s(t) = at^2 + bt + c is constant, with a value of 2a.