Final answer:
As the speed of the car decreases, the magnitude of the centripetal force will also decrease because it is proportional to the square of the vehicle's speed.
Step-by-step explanation:
If the speed of the car decreases, the magnitude of the centripetal force acting on the car as it travels around the curve will also decrease. This change occurs because the centripetal force (Fc) is directly proportional to the square of the speed (v) of the vehicle and is calculated using the formula Fc = mv²/r, where m is the mass of the car, v is the velocity, and r is the radius of the curve. Since the mass (m) and radius (r) remain constant, a decrease in velocity (v) leads to a decrease in centripetal force.
To further illustrate, given a centripetal acceleration (ac) of 1.8 m/s² and a car mass (m) of 1,200 kilograms, the centripetal force can be calculated as Fc = mac. During a decrease in speed, while the radius (r) stays at 45 meters, the decrease in velocity reduces the acceleration (ac), hence, the centripetal force will be less.
This is due to the fact that the centripetal force required to keep the car moving in a circle is dependent on the velocity: at lower speeds, less force is required to maintain circular motion.