A car of mass 1190 kg is on an icy driveway inclined at an angle of 28◦ If the incline is frictionless, what is the acceleration of the car?

To find the acceleration of the car on the icy inclined driveway, we can use Newton's second law of motion.

Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The net force on the car can be determined by analyzing the forces acting on it.

In this case, the only force acting on the car is its weight, which can be resolved into two components: the force acting downhill (parallel to the incline) and the force acting perpendicular to the incline.

The force acting downhill can be calculated using the formula: F_downhill = m * g * sin(θ), where m is the mass of the car, g is the acceleration due to gravity (approximately 9.8 m/s²), and θ is the angle of the incline (28°).

F_downhill = 1190 kg * 9.8 m/s² * sin(28°)
F_downhill ≈ 1190 kg * 9.8 m/s² * 0.469 (rounded to three decimal places)
F_downhill ≈ 5524.892 N (rounded to three decimal places)

Since the incline is frictionless, the force acting perpendicular to the incline is zero.

Now, we can use Newton's second law to calculate the acceleration:

F_net = m * a
a = F_net / m

Since the net force acting on the car is the force acting downhill:

a = F_downhill / m
a = 5524.892 N / 1190 kg
a ≈ 4.641 m/s² (rounded to three decimal places)

Therefore, the acceleration of the car on the icy inclined driveway is approximately 4.641 m/s².