No, the acceleration of a car will not be the same when it travels around a sharp curve compared to when it travels around a gentle curve at the same speed. The curvature of the curve, represented by the radius of the circle, affects the magnitude of the centripetal acceleration experienced by the car.
Centripetal acceleration (ac) is the acceleration directed toward the center of the circular path that keeps an object moving in a curved path. It is given by the formula:
ac = v^2 / r
where v is the velocity of the car and r is the radius of the curve.
In the case of a car traveling around a sharp curve, the radius of the curve is small. Since the centripetal acceleration is inversely proportional to the radius, a smaller radius will result in a larger centripetal acceleration. Therefore, the car will experience a higher acceleration when navigating a sharp curve at a constant speed.
On the other hand, when the car travels around a gentle curve with a larger radius, the centripetal acceleration will be smaller compared to the sharp curve scenario. The larger radius reduces the magnitude of the centripetal acceleration, resulting in a lower acceleration experienced by the car.
It's important to note that the car is still traveling at the same speed (60 km/h) in both cases, but the acceleration differs due to the difference in the curvature of the curves. The sharp curve requires a higher acceleration to maintain the car's trajectory, while the gentle curve requires a relatively smaller acceleration.
In summary, the acceleration of a car will be different when traveling around a sharp curve compared to a gentle curve at the same speed due to the difference in the radius of curvature. The sharp curve will result in a higher centripetal acceleration, while the gentle curve will have a lower centripetal acceleration.