The body moves along the ОХ axis so that its coordinates change over time according to the law x = -5 + 3t-0.1t ^ 2

| February 23, 2021 | education

The body moves along the ОХ axis so that its coordinates change over time according to the law x = -5 + 3t-0.1t ^ 2 (coordinates are given in meters). What is the acceleration in the body? At what point in time is the speed of the body equal to 2 m / s?

Given: the law of variation of the coordinates of the body under consideration along the OX axis: x (t) = -5 + 3t – 0.1t2; V (considered speed of movement) = 2 m / s.

1) The law of speed change: V (t) = x (t) ‘= (-5 + 3t – 0.1t ^ 2)’ = -0 + 3 * 1 – 0.1 * 2t = 3 – 0.2t.

2) Time to reach a speed of 2 m / s: 2 = 3 – 0.2t, whence we express: t = (3 – 2) / 0.2 = 5 s.

3) Constant acceleration: a (t) = V (t) ‘= (3 – 0.2t)’ = 0 – 0.2 * 1 = -0.2 m / s2.

Answer: Constant acceleration is -0.2 m / s2; the body will reach a speed of 2 m / s 5 s after the start of its movement.



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