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The equation for the acceleration of a body moving in a circle is [tex]a = \frac{v^{2} }{r}[/tex], where a is acceleration, v is velocity and r is the radius of the circle. Acceleration has units of m/[tex]s^{2}[/tex].

a. What is the acceleration of a body moving with a velocity of 30 m/s in a circle of radius 10 m?

b. Solve the equation for velocity

c. What is the velocity of a body that has an acceleration of 20 m/[tex]s^{2}[/tex] and is moving in a circle of radius 2 m?

Respuesta :

person150752

a. Since the acceleration equation is given to us, we can just plug in:

[tex]a = \frac{30^{2} }{10} =\frac{900}{10} = 90[/tex] m/s²

b. Use algebra:

[tex]a = \frac{v^2}{r}[/tex]

[tex]ra = v^2[/tex]

[tex]v = \sqrt{ra}[/tex]

c. Use the equation derived in b and plug in:

[tex]v = \sqrt{20(2)} = \sqrt{40} = 6.32455532[/tex] m/s

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