The dependence of the path traveled by the body along a circle with radius r = 5 cm is given by the equation

| February 15, 2021 | education

The dependence of the path traveled by the body along a circle with radius r = 5 cm is given by the equation s = ct ^ 3, where c = 0.01 m / s ^ 3. determine for the moment when the body speed V = 0.5 m / s, normal and tangential acceleration

The radius of the circle is r = 5 cm = 0.05 m.

Velocity is the first derivative of the path equation.

s = c * t ^ 3. v = ds / dt = 3 * c * t ^ 2 = 3 * 0.01 * t ^ 2 = 5 m / s.

We solve the equation 3 * 0.01 * t ^ 2 = 5, we get t = 12.9 s. After 12.9 seconds, the body will pick up this speed.

We find the normal acceleration by the formula an = v ^ 2 / r = 5 ^ 2 / 0.05 = 500 m / s ^ 2.

Tangential acceleration is the second derivative of the path equation and the first derivative of the velocity equation.

at = dv / dt = 6 * c * t = 6 * 0.01 * 12.9 = 0.77 m / s ^ 2.



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