15. (ufpe) a figura a seguir mostra um bloco de massa 10 kg,
apoiado sobre uma superfície horizontal. ao longo da dire-
ção horizontal, indicada pelo eixo x, o bloco encontra-se sob
a ação de uma força constante de módulo fe de uma força
constante de módulo 30 n no sentido oposto. a equação
horária da posição do bloco é dada pela expressão x =
= 150 + 12t -0,60t2, onde x é dado em metros, et é dado
em segundos. qual é o valor de f em newtons?

18 N

Explanation:

According to the described situation, the net force in the Y component is zero and we will work only with the X component.

We have a block with mass and two forces acting on it. which are and in the opposite direction, so the net force acting on the object is:

(1)

In addition:

(2)

On the other hand, acceleration is the result of the second derivative of the position with respect to time, this means we have to derive twice the following equation:

(3) Being the position in meters and the time in seconds.

Let's derive (3) and find the velocity :

(4)

(5) This is the velocity

Now, let's derive (5) and find the acceleration:

(6)

(7) This is the acceleration

Substituting (7) in (2):

(8)

(9) This is the value of the net force

Substituting (9) in (1):

(10)

Finally finding :

(11)

report!

explanation:

physics means: "the branch of science concerned with the nature and properties of matter and energy. the subject matter of physics, distinguished from that of chemistry and biology, includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms."