Question

A race car goes around a level, circular track with a diameter of 1.00 km at a constant speed of 89 km/h. What is the car's centripetal acceleration in m/s^2?

Answer 1

To find the car's centripetal acceleration, convert the speed to meters per second, then use the formula a = v^2 / r. With a speed of 24.71 m/s and a track radius of 500 m, the acceleration is approximately 1.22069 m/s².

Step-by-step explanation:

The student is asking to determine the centripetal acceleration of a race car moving at a constant speed along a circular track. To calculate this, we can use the formula for centripetal acceleration: a = v^2 / r. First, we need to convert the speed from km/h to m/s, which can be done by multiplying by ⅟ (≅ 0.27778). Thus, 89 km/h equates to 89 × 0.27778 m/s, which is about 24.71 m/s. The diameter of the track is 1.00 km (1000 m), hence the radius r is half of that, 500 m.

Using the formula:

a = (24.71 m/s)² / 500 m

a = 610.3441 m²/s² / 500 m

a = 1.22069 m/s² (approximately)

The centripetal acceleration of the race car is approximately 1.22069 m/s².

Answer 2

The car's centripetal acceleration is 1.22 m/s².

Step-by-step explanation:

Given that,

Diameter of circular track
`d= 1.00\ km=1000\ m`

Radius r = 500 m

Constant speed
`v = 89\ km/h = 89*(5)/(18)=24.722\ m/s`

The centripetal acceleration is defined as,

`a_(c) = (v^2)/(r)`

Where, v = tangential velocity

r = radius

Put the value into the formula

`a_(c)=((24.722)^2)/(500)`

`a_(c)=1.22\ m/s^2`

Hence, The car's centripetal acceleration is 1.22 m/s².