Final answer:
Braking distance is generally longer on surfaces with less friction, such as wet roads, not necessarily smoother roads. Factors such as road conditions, tyre grip, and driver reaction time play a significant role in determining stopping distances.
Step-by-step explanation:
The statement that braking distance is greater on a smooth road is generally false. The distance necessary to stop a car does indeed vary greatly, depending on road conditions and driver reaction time. However, the coefficient of friction plays a crucial role in this. A smooth road typically offers less friction compared to a road with a rougher surface such as a gravel road. When the road is smoother, the tyres may not grip the road as effectively, leading to longer braking distances. Yet, it's important to note that modern road surfaces are designed to maintain a good level of friction even when they appear smooth.
Figures and examples from the textbook attributes like position x (m) show that the friction, whether on dry or wet pavement, affects stopping distance significantly. Consider a car initially traveling at 30.0 m/s; it will have different stopping distances based on whether the pavement is dry or wet, with longer distances generally required on wet roads due to lower friction. The reaction time of the driver also adds to the overall stopping distance, but the primary factor is the interaction between the tyres and the road surface.