Mathematics: The centripetal acceleration of an object moving uniformly in a circle varies inversely with the radius of the circle. If the object feels acceleration of 20 m/s2 when the radius is 4 m, find the acceleration when the radius is 5 m.

B.) (-8,0)Step-by-step explanation:...

The centripetal acceleration of an object moving uniformly

payton05

29.01.2022

a_c=16m/s^2

Step-by-step explanation:

the centripetal acceleration is defined by the following formula:

a=v^2/r

where v is the tangential velocity, and r is the radius.

if we have an acceleration of 20m/s^2 and a radius of 4m the equation becomes:

20m/s^2=v^2/(4m)

and from here we can find the tangential velocity of the object:

$v^2=(20m/s^2)(4m)\\v^2=80m^2/s^2$

we can use this quantity to find the centripetal acceleration when the radius is 5m.

Again using the centripetal acceleration formula:

a=v^2/r

we substitute v^2 and r=5m :

$a_c=(80m^2/s^2)/(5m)\\a_c=16m/s^2$

the centripetal acceleration is 16 m/s^2

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