The equation of motion of a body moving along the OX axis has the form: X = 4 + 2t + t ^ 2.

| September 26, 2021 | education

The equation of motion of a body moving along the OX axis has the form: X = 4 + 2t + t ^ 2. After what time will the speed of the body be equal to 18 m / s?

The equation of body motion, which can be used to determine the position of the body x at any moment of time t, is generally written in the form of equality: x = x₀ + v₀ ∙ t + a ∙ t ^ 2/2, where x₀ is the coordinate of the initial location of the body, v₀ is the initial speed, and is the acceleration. From the condition of the problem it is known that the equation of motion of a body moving along the Ox axis has the form: x = 4 + 2 ∙ t + t ^ 2, hence, comparing the coefficients with the equation of body motion in general form, we obtain:

v₀ = 2 m / s, a = 2 m / s ^ 2.

To find the time after which the speed of the body will be equal to v = 18 m / s, we use the formula t = (v – v₀) / a. Substitute the values ​​of physical quantities in the calculation formula:

t = (18 m / s – 2 m / s) / 2 m / s ^ 2 or t = 8 s.

Answer: after 8 seconds (3) the speed of the body will be equal to v = 18 m / s.



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