Question

Под действием силы F=50 Н тело движется прямолинейно так, что зависимость пройденного телом пути s от времени t задаётся уравнением s(t)=5-2t+4t^2м. Найти массу m тела. И пожалуйста объясните.

Answer 1

S(t)=So+Vo*t+a*t²/2
Запишем наше уравнение в виде:
S(t)=5 + (-5)*t + 8*t²/2

Тогда сразу из формулы получаем 
a = 8 м/с²

m=F/a = 50/8 = 6,25 кг

Answer 2

Problem Analysis

We are given that a body is moving in a straight line under the influence of a force F = 50 N. The equation that describes the relationship between the distance traveled by the body (s) and the time (t) is given as s(t) = 5 - 2t + 4t^2. We need to find the mass (m) of the body.

Solution

To find the mass of the body, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the force acting on the body is given as F = 50 N.

From the equation s(t) = 5 - 2t + 4t^2, we can determine the acceleration of the body by taking the second derivative of s(t) with respect to time (t). The second derivative represents the acceleration.

Let's calculate the second derivative of s(t):

s(t) = 5 - 2t + 4t^2

Taking the first derivative:

s'(t) = -2 + 8t

Taking the second derivative:

s''(t) = 8

The second derivative s''(t) is a constant value of 8, which represents the acceleration of the body.

Now, we can use Newton's second law to find the mass of the body. Rearranging the equation, we have:

F = m * a

Substituting the values:

50 N = m * 8

Solving for m:

m = 50 N / 8

m ≈ 6.25 kg

Therefore, the mass of the body is approximately 6.25 kg.

Conclusion

The mass of the body is approximately 6.25 kg. This is calculated using Newton's second law of motion, where the force acting on the body is given as 50 N and the acceleration is determined from the second derivative of the distance-time equation.