Question

A race car moving with a constant speed of 60 m/s completes one lap around a circular track in 50 s. What is the magnitude of the acceleration of the race car? 8.8 m/s2 7.5 m/s2 9.4 m/s2 6.3 m/s2 5.3 m/s2

Answer 1

To find the magnitude of the acceleration of the race car we can use the equation for centripetal acceleration:

a = (v^2) / r

where:

a = acceleration

v = velocity

r = radius of the circular track

Given:

v = 60 m/s

t = 50 s

To find the radius of the circular track we can use the formula:

circumference = 2πr

Since the car completes one lap in 50 seconds the distance traveled is equal to the circumference of the circular track.

distance = circumfrance = 2πr

Since the velocity is constant the distance traveled can also be calculated by multiplying the velocity by the time:

distance = v * t

Therefore we have:

2πr = v * t

Solving for r:

r = (v * t) / (2π)

Plugging in the given values:

r = (60 m/s * 50 s) / (2π)

r ≈ 477.46 meters

Now we can calculate the magnitude of the acceleration:

a = (v^2) / r

a = (60 m/s)^2 / 477.46 meters)

a ≈ 7.54 m/s^2

Therefore the magnitude of the acceleration of the race car is approximately 7.54 m/s^2.

Out of the given options the closest value to this result is 7.5 m/s^2.

Answer 2

The magnitude of the centripetal acceleration of a race car moving with a constant speed of 60 m/s and completing one lap in 50 seconds is approximately 7.54 m/s², calculated using the centripetal acceleration formula a = v²/r.

The question pertains to centripetal acceleration and asks what the magnitude of the acceleration of a race car is if it moves with a constant speed of 60 m/s and completes one lap around a circular track in 50 seconds.

To find the centripetal acceleration, you use the formula:

a = v²/r

where a is the centripetal acceleration, v is the constant speed, and r is the radius of the circular path.

Since the car completes one lap in 50 seconds, we can find the circumference of the track (which is 2πr) by multiplying the speed by the time:

Circumference = speed × time = 60 m/s × 50 s = 3000 m

Now, to find the radius:

r = Circumference / (2π) = 3000 m / (2π) ≈ 477.46 m

Finally, we calculate the centripetal acceleration:

a = (60 m/s)² / 477.46 m ≈ 7.54 m/s²

Therefore, the magnitude of the centripetal acceleration is approximately 7.54 m/s².