Question

11. A car moving at 30.0 km/h rounds a bend in the road that has a radius of 21.2 m. What is the

centripetal acceleration of the car?

Answer 1

The centripetal acceleration of the car is
`3.276`
`m/s^2`.

Step-by-step explanation:

Centripetal Acceleration Equation

`a_c=(v^2)/(r)`

Lets convert
`((km/h)^2)/(m)` to
`(m)/(s^2)`

First convert km/h to m/s. We can use the following relationships.

1 km = 1000 m

1 hour = 60 min

1 min = 60 sec

`(km)/(h)` to
`(m)/(s)`

`(1*1000)/(1*60*60)` simplifies to
`(5)/(18)`.

Now we have
`((m/s)^2)/(m)`

`((m^2)/(s^2) )/(m)`

Multiply the numerator by the reciprocal of the denominator.

`(m^2)/(s^2)*(1)/(m)`

Combine.

`(m^2*1)/(s^2m)`

Factor
`m` out of
`m^2*1`.

`(m(m*1))/(m*s^2)`

Cancel the common factor.

`(m)/(s^2)`

Multiply the speed value in km/h by
`(5)/(18)` to get the speed value in m/s.

`a_c=((30*(5)/(18))^2 )/(21.2)`

`a_c=(((25)/(3) )^2 )/(21.2)`

`a_c=((625)/(9) )/(21.2)`

`a_c=3.276`
`m/s^2`