The equation of its motion is s = t ^ 4 + 2t ^ 2 + 5. Determine the instantaneous speed

| April 26, 2021 | education

The equation of its motion is s = t ^ 4 + 2t ^ 2 + 5. Determine the instantaneous speed and acceleration of the point at the end of the second second from the start of movement, the average speed and the distance traveled during this time.

S (t) = t ^ 4 + 2 * t ^ 2 + 5.

t = 2 s.

V -?

a -?

Vav -?

S -?

S = (2) ^ 4 + 2 * (2) ^ 2 + 5 = 29 m.

The dependence of speed on time V (t) is the derivative of the dependence of displacement on time S (t) “: V (t) = S (t)” = (t ^ 4 + 2 * t ^ 2 + 5) “= 4 * t ^ 3 + 4 * t.

V = 4 * (2) ^ 3 + 4 * 2 = 40 m / s.

The dependence of the acceleration of a body on time a (t) is the derivative of the dependence of its speed on time V (t) “: a (t) = V (t)” = (4 * t ^ 3 + 4 * t) = 12 * t ^ 2 + 4.

a = 12 * (2) ^ 2 + 4 = 52 m / s2.

We find the average speed by the formula: Vav = S / t.

Vav = 29 m / 2 s = 14.5 m / s.

Answer: V = 40 m / s, a = 52 m / s2, S = 29 m, Vav = 14.5 m / s.



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