Step 1: Identify the force and apply Newton's second law to find acceleration.
A constant force $F = 5$ N acts on a body of unknown mass $m$. By Newton's second law: \[ F = ma \implies a = \frac{F}{m} = \frac{5}{m} \, \text{ms}^{-2} \] Since the force is constant, the acceleration is also constant throughout the motion.
Step 2: Find the velocity of the body at $t = 3$ s.
The body starts from rest, so initial velocity $u = 0$. Using the kinematic equation $v = u + at$: \[ v = 0 + \frac{5}{m} \times 3 = \frac{15}{m} \, \text{ms}^{-1} \] This is the velocity of the body exactly 3 seconds after the force is applied.
Step 3: Use the definition of instantaneous power.
Instantaneous power is the rate of doing work at a particular instant. For a constant force $F$ and instantaneous velocity $v$: \[ P = Fv \] This follows from $P = dW/dt = F \cdot dx/dt = F \cdot v$.
Step 4: Apply the given power condition at $t = 3$ s.
We are told that at $t = 3$ s, the instantaneous power is $P = 5$ W. Substituting: \[ 5 = 5 \times \frac{15}{m} = \frac{75}{m} \]
Step 5: Solve for the mass $m$.
\[ m = \frac{75}{5} = 15 \, \text{kg} \]
Step 6: Verify the result by checking consistency.
With $m = 15$ kg: acceleration $= 5/15 = 1/3 \, \text{ms}^{-2}$; velocity at $t = 3$ s is $= (1/3) \times 3 = 1 \, \text{ms}^{-1}$; instantaneous power $= 5 \times 1 = 5$ W. This matches the given data perfectly, confirming our answer. \[ \boxed{m = 15 \, \text{kg}} \]