The equation of motion of a material point has the form x = A + Bt ^ 2 + Ct ^ 4,

| September 23, 2021 | education

The equation of motion of a material point has the form x = A + Bt ^ 2 + Ct ^ 4, where B = 5m / s ^ 2, C = -0.3m / s ^ 4. find the speed of a material point at time 2 s.

x (t) = A + B * t ^ 2 + C * t ^ 4.

B = 5 m / s2.

C = – 0.3 m / s4.

t = 2 s.

Vx -?

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

Let us find the derivative of the coordinate dependence: Vx (t) = (A + B * t ^ 2 + C * t ^ 4) “= 2 * B * t + 4 * C * t3.

Vx (t) = 2 * 5 m / s2 * t + 4 * (- 0.3 m / s4) * t ^ 3 = 10 m / s2 * t – 1.2 m / s ^ 4 * t ^ 3.

Vx (2 s) = 10 m / s2 * 2 s – 1.2 m / s ^ 4 * (2 s) ^ 3 = 20 m / s – 9.6 m / s = 10.4 m / s.

Answer: the speed of a material point will be Vx = 10.4 m / s.



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