An object travels in a circular path of radius 5.0 meters at a uniform speed of 10. m/s. what is the magnitude of the object's acceleration? 2.0 m/s/s 2.5 m/s/s 5.0 m/s/s 20. m/s/s 50. m/s/s

a = 20 m/s²

Explanation:

The magnitude of the acceleration of an object that moves in a circular path is given by:

Formula (1)

where:  

at = α*R : Formula (2)  :Tangential acceleration

ac = ω²*R :  Formula (3) : Centripetal acceleration

α : angular acceleration (rad/s²)  

ω: angular speed  (rad/s)  

R : is radius where the object is located from the center of the circular path

The tangential velocity of the body is calculated as follows:

v = ω*R  Formula (4)

where:  

v is the tangential velocity or linear velocity (m /s)  

ω is the angular speed (rad/s)  

R is radius where the body is located from the center of the circular path

Data

v = 10 m/s : tangential speed of the object (uniform)

R = 10 m

Calculating of ω  (angular speed)

We replace data in the formula (4)

v = ω*R

10 = ω*5

ω = 10 / 5

ω = 2 rad/s

Calculating of the Centripetal acceleration (ac)

We replace ω = 2 rad/s in the formula (3)

ac = ω²*R

ac = (2)²*(5)

ac = 20 m/s²

Calculating of  the tangential acceleration (at)

Because the magnitude of the tangential speed is uniform , then α=0

We replace α=0  in the formula (2)

at =α*R = 0*5

at = 0

Calculating of  the magnitude of the object's acceleration (a)

We replace :  at = 0 and ac = 20 m/s²  in the formula (1)

a = 20 m/s²

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