The projection of the velocity of the body moving along the x axis is given by the equation Vx = 8-2t.

The projection of the velocity of the body moving along the x axis is given by the equation Vx = 8-2t. Point out which of the four statements are correct and which are not. it is necessary to explain each statement A. For the first 2 s of motion, the x coordinate of the body changed by 12 m B. The x coordinate of the body changes according to the law: x = 8-2t C. The body moves uniformly D. In 4 s after the start of the movement, the speed of the body will be equal to zero

Given:

v (t) = 8 – 2 * t – the equation of the dependence of speed on time.

You want to validate the claims specified in the task description.

Let’s define the equation of body motion:

Let’s find the initial speed of the body, at t = 0;

v0 = 8 – 2 * 0 = 8 – 0 = 8 meters per second.

Let us find the acceleration by fulfilling the first-degree derivative of the equation for the dependence of speed on time:

a = v (t) ’= (8 – 2 * t)’ = -2 meters per second squared.

Then the equation of motion of the body will be:

x (t) = v * t + a * t2 / 2 = 8 * t + (-2) * t2 / 2 =

= 8 * t – t2.

Let’s check the first statement:

x (t) = 8 * t – t2 = 8 * 2 – 22 = 16 – 4 = 12 meters, that is, the statement is correct.

Let’s check the second statement:

Since the coordinate of the body changes according to the law x (t) = 8 * t – t2, the statement is incorrect.

Let’s check the third statement:

Since the acceleration of the body is not zero, the motion cannot be uniform, that is, the statement is incorrect.

Let’s check the fourth statement:

v = 8 – 2 * t = 8 – 2 * 4 = 8 – 8 = 0, that is, the statement is true.

Answer: statements A and D are correct, B and C are not true.