I need help with conversions. I am not sure the formulas

Question

A car travels at a constant spped of 95.0 kilometers per hour around a circular track with a diameter of 1.00 kilometers. What is the magnitude of the car's centripetal acceleration in units of m/s squared

Answer 1

The centripetal acceleration of an object traveling in a circle is equal to v²/r, where v is the speed and r is the radius of the circle.

 

In this case, you have to make three adjustments to the numbers they give you.

 

1. They give you the diameter, so you have to divide it by 2 to get the radius. So r = 0.5 km.

2. Then you have to convert that to meters, since they want the result in m/s.  There are 1000 meters in a kilometer, so 0.5 km = 500 m.

3. They give you the speed in km/hour.  First convert the speed to km/s:  There are 60 minutes in an hour and 60 seconds in a minute, so there are 60 x 60 = 3600 seconds in an hour.  So 95 km/h = 95 km / 3600 s = 0.02639 km / s.  Then convert to meters by multiplying by 1000 again.  0.02639 km / s = 26.39 m/s

 

Now use the formula:  v²/r = (26.39 m/s)²/ 500 m = 1.393 m/s²

 

 

 

Answer 2

Acceleration is Velocity squared x radius of the curvature

[95 km/hour x (1000 m / km) x (hour / 60 minutes) x (minute / 60 seconds)]^2 / { 1km x (1000m / 1 km)} 

 

= 0.6937 m/s^2

 

 

https://en.wikipedia.org/wiki/Centripetal_force