A car can be driven around a 120 m radius curve at constant speed without sliding if the maximum centripetal acceleration is 0.130g.

(a) What is the maximum speed that the car can travel around the curve without sliding?
(b) If the car was on a circular race track with this same radius, how long would it take for the car to complete one lap at the maximum speed?

To solve this problem, we need to use the centripetal acceleration formula:

a = v² / r

where:
a is the centripetal acceleration,
v is the velocity, and
r is the radius of the curve.

(a) First, let's find the maximum speed that the car can travel around the curve without sliding.

Given:
Maximum centripetal acceleration (a) = 0.130g
Radius of the curve (r) = 120 m

To convert the centripetal acceleration from g to m/s², we need to know the value of the acceleration due to gravity (g). In this case, we'll assume it is approximately 9.8 m/s², which is the standard value on Earth.

Substituting the values into the formula, we have:
0.130g = v² / r

Rearranging the equation, we can solve for v:
v² = 0.130g * r

Taking the square root of both sides, we get:
v = √(0.130g * r)

Plugging in the values:
v = √(0.130 * 9.8 * 120)

Calculating the maximum speed:
v ≈ 13.99 m/s

Therefore, the maximum speed that the car can travel around the curve without sliding is approximately 13.99 m/s.

(b) To find the time it takes for the car to complete one lap, we need to know the circumference of the circular race track.

The circumference (C) of a circle is given by the formula:
C = 2πr, where r is the radius.

Plugging in the value of the radius (r = 120 m):
C = 2π * 120

The time it takes to complete one lap (T) is given by the formula:
T = C / v, where v is the velocity.

Plugging in the values:
T = (2π * 120) / 13.99

Calculating the time to complete one lap:
T ≈ 54.01 seconds

Therefore, it would take approximately 54.01 seconds for the car to complete one lap at the maximum speed.