The question asks about a crate being pulled up a rough incline with an initial speed and a given pulling force. To find the acceleration of the crate, we need to consider the forces acting on it.
The weight of the crate can be calculated using the formula: weight = mass × acceleration due to gravity. Since the mass is given as 9.8 kg, and the acceleration due to gravity is approximately 9.8 m/s², the weight of the crate is 9.8 kg × 9.8 m/s² = 96.04 N.
The force applied parallel to the incline is 102 N. To find the net force acting on the crate, we need to subtract the frictional force opposing the motion. The frictional force can be calculated using the formula: frictional force = coefficient of friction × normal force.
Since the crate is being pulled up the incline, the normal force is equal to the weight of the crate. Therefore, the frictional force is given by the formula: frictional force = coefficient of friction × weight. However, the coefficient of friction is not provided in the question, so we cannot determine the exact value of the frictional force.
Given that the crate has an initial speed of 1.44 m/s, we can assume that the frictional force is equal to the force of kinetic friction, which can be calculated using the formula: force of kinetic friction = coefficient of kinetic friction × normal force.
Without knowing the coefficient of kinetic friction, we cannot calculate the exact value of the force of kinetic friction. However, we can determine the acceleration of the crate using the formula: acceleration = (net force - force of kinetic friction) / mass.
To summarize, we have determined the weight of the crate as 96.04 N, the force applied parallel to the incline as 102 N, and the initial speed of the crate as 1.44 m/s. However, without the coefficient of kinetic friction, we cannot calculate the exact value of the acceleration of the crate.