Final answer:
To find the acceleration of an object sliding down an incline, you need to consider the forces acting on it. These forces include the component of gravity along the incline and the frictional force opposing motion. By using the formula a = g * (sin(theta) - u * cos(theta)), where g is the acceleration due to gravity, theta is the angle of the incline, and u is the coefficient of kinetic friction, you can calculate the acceleration. In this case, the acceleration is approximately 4.2 m/s².
Step-by-step explanation:
To find the acceleration of the object sliding down the incline, we need to consider the forces acting on it. The force due to gravity can be resolved into two components: one parallel to the incline and one perpendicular to the incline. The component parallel to the incline, which causes acceleration, is given by F = m * g * sin(theta), where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s²), and theta is the angle of the incline.
Next, we need to consider the frictional force opposing the motion. The frictional force is given by F_friction = u * m * g * cos(theta), where u is the coefficient of kinetic friction.
The net force acting on the object is the difference between the force due to gravity and the frictional force. Therefore, the acceleration of the object is given by a = (m * g * sin(theta) - u * m * g * cos(theta)) / m = g * (sin(theta) - u * cos(theta)).
Plugging in the values, we have a = 9.8 m/s² * (sin(45°) - 0.60 * cos(45°)) ≈ 4.2 m/s².