The equation of motion of a material point has the form x = 0.4 t ^ 2. Find the speed in general form (formulas)

| May 17, 2021 | education

The equation of motion of a material point has the form x = 0.4 t ^ 2. Find the speed in general form (formulas) and calculate the distance traveled by the point in 4 s?

x (t) = 0.4 * t^2.

t = 4 s.

V (t) -?

S -?

The dependence of the speed of movement of the body on time V (t) is the derivative of the dependence of the coordinate on time x (t): V (t) = x (t) “.

V (t) = (0.4 * t ^ 2) “= 0.4 * 2 * t = 0.8 * t – uniformly accelerated motion with acceleration a = 0.8 m / s2.

V (4 s) = 0.8 * 4 = 3.2 m / s.

Since the movement occurs along the OX coordinate axis, the path S traversed by the body will be determined by the formula: S = x – x0.

x (4 s) = 0.4 * (4) ^ 2 = 6.4 m.

x (0 s) = 0.4 * (0) ^ 2 = 0 m.

S = 6.4 m – 0 m = 6.4 m.

Answer: V (t) = 0.8 * t, V = 3.2 m / s, S = 6.4 m.



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