The ideal angle of banking provided on the curves on roads depends upon the velocity squared (velocity^2) of the vehicle.

Velocity squared (velocity^2) of the vehicle is the correct answer because it directly affects the centripetal force acting on the vehicle as it negotiates a curve. The centripetal force is the force that keeps an object moving in a curved path and is directed towards the center of the curve.

When a vehicle enters a curve, the centripetal force required to keep the vehicle moving in a curved path is provided by the friction between the tires and the road surface. This friction force is proportional to the normal force between the tires and the road surface, which is determined by the weight of the vehicle.

The centripetal force can be calculated using the formula:

Fc = (mv^2) / r

Where Fc is the centripetal force, m is the mass of the vehicle, v is the velocity of the vehicle, and r is the radius of the curve.

From this equation, it is clear that the centripetal force is directly proportional to the square of the velocity (v^2). Therefore, in order to maintain a constant centripetal force and prevent the vehicle from skidding or slipping, the angle of banking on the curve should be adjusted according to the velocity of the vehicle.

The angle of banking can be calculated using the formula:

θ = tan^-1 (v^2 / (g * r))

Where θ is the angle of banking, v is the velocity of the vehicle, g is the acceleration due to gravity, and r is the radius of the curve.

This equation shows that the angle of banking is directly proportional to the velocity squared (v^2). As the velocity increases, the angle of banking should also increase in order to provide the necessary centripetal force to keep the vehicle on the curve without skidding or slipping.

Therefore, the ideal angle of banking provided on the curves on roads depends upon the velocity squared (velocity^2) of the vehicle.

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