Two forces (2i - 5j)N and (-3i + 4j)N act on a body of mass 5kg. Find in \(ms^{-2}\), the magnitude of the acceleration of the body.

Answer Details

To find the magnitude of acceleration, we need to use Newton's Second Law, which states that the force acting on an object is equal to its mass multiplied by its acceleration. In this case, we have two forces: (2i - 5j)N and (-3i + 4j)N. To find the net force, we add these two vectors by adding their corresponding components: (2i - 5j)N + (-3i + 4j)N = -i - j N So the net force is (-i - j)N. Now, using Newton's Second Law, we can find the acceleration: F = ma where F is the net force, m is the mass, and a is the acceleration. In our case, the net force is (-i - j)N and the mass is 5kg, so we have: (-i - j)N = 5kg * a Solving for a, we get: a = (-i - j)N / 5kg To find the magnitude of a, we take the square root of the sum of the squares of its components: |a| = sqrt((-1)^2 + (-1)^2) N/kg = sqrt(2) N/kg Converting to \(ms^{-2}\) by dividing by 5, we get: |a| = sqrt(2)/5 \(ms^{-2}\) Therefore, the answer is \(\frac{\sqrt{2}}{5}\).