To find the maximum speed the car can safely travel around the curve without skidding, we need to consider the centripetal force and the maximum frictional force.

The centripetal force acting on the car is provided by the frictional force between the tires and the road. The formula for centripetal force is:

Fc = mv² / r

Where:
Fc = centripetal force
m = mass of the car
v = velocity of the car
r = radius of the curve

The maximum frictional force can be calculated using the formula:

Ffriction = μN

Where:
Ffriction = frictional force
μ = coefficient of friction between the tires and the road
N = normal force

The normal force acting on the car is equal to the gravitational force acting on the car, which can be calculated using the formula:

N = mg

Where:
N = normal force
m = mass of the car
g = acceleration due to gravity (approximately 9.8 m/s²)

Since the car is not skidding, the maximum frictional force will be equal to the centripetal force. Thus, we have:

Fc = Ffriction

mv² / r = μN
mv² / r = μmg
v² = μrg
v = √(μrg)

Now we can substitute the given values into the formula to calculate the maximum speed:

μ = 0.4 (coefficient of friction)
r = 50 meters (radius of the curve)
g = 9.8 m/s² (acceleration due to gravity)

v = √(0.4 * 50 * 9.8)
v = √(196)
v ≈ 14.0 m/s

Therefore, the maximum speed the car can safely travel around the curve without skidding is approximately 14.0 m/s.

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