Question

Шарик равномерно движется по окружности радиусом 3м,совершая полный оборот за 10с.Определите его скорость и ускорение.

Answer 1

скорость

$v= \frac{2 \pi R}{T}$

$v= \frac{2* \pi *3}{10} = 0.6 \pi =1.884m/s$ Ответ

ускорение

$a= \frac{v ^{2} }{R} = \frac{4 \pi ^{2} R ^{2} }{T ^{2} R} =\frac{4 \pi ^{2} R}{T ^{2} } = \frac{4*10*3}{100} =1.2m/s ^{2}$ Ответ

Answer 2

Given Information:

A ball is moving uniformly in a circle with a radius of 3 meters. It completes one full revolution in 10 seconds.

Velocity:

The velocity of an object moving in a circle is given by the formula:

v = (2πr) / T

Where: - v is the velocity - π is a mathematical constant approximately equal to 3.14159 - r is the radius of the circle - T is the time taken to complete one revolution

Substituting the given values into the formula:

v = (2π * 3) / 10

Calculating the velocity:

v ≈ 1.88496 m/s.

Therefore, the velocity of the ball is approximately 1.88496 m/s.

Acceleration:

The acceleration of an object moving in a circle is given by the formula:

a = (v^2) / r

Where: - a is the acceleration - v is the velocity - r is the radius of the circle

Substituting the given values into the formula:

a = (1.88496^2) / 3

Calculating the acceleration:

a ≈ 1.25497 m/s^2.

Therefore, the acceleration of the ball is approximately 1.25497 m/s^2.

To summarize: - The velocity of the ball is approximately 1.88496 m/s. - The acceleration of the ball is approximately 1.25497 m/s^2.