If the only forces acting on a 3.0-kg mass are F1 = (3i - 8j) N and F2 = (5i + 3j) N, what is the magnitude of the acceleration (in m/s2) of the particle?

To solve this problem, we need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula is F = ma, where F is the net force, m is the mass, and a is the acceleration.

Step 1: Calculate the net force. The net force is the vector sum of all the forces acting on the object. In this case, we have two forces, F1 and F2. We add these two forces together:

F_net = F1 + F2 = (3i - 8j) N + (5i + 3j) N = (3+5)i + (-8+3)j = 8i - 5j N

Step 2: Calculate the acceleration. We rearrange the formula F = ma to solve for acceleration: a = F/m. We substitute the values we have:

a = F_net / m = (8i - 5j) N / 3.0 kg = 8/3 i - 5/3 j m/s²

Step 3: Calculate the magnitude of the acceleration. The magnitude of a vector is given by the formula √(x² + y²), where x and y are the components of the vector. In this case, x = 8/3 and y = -5/3:

|a| = √[(8/3)² + (-5/3)²] = √[(64/9) + (25/9)] = √(89/9) = √9.89 = 3.14 m/s²

So, the magnitude of the acceleration of the particle is approximately 3.14 m/s².