Question
A 5 kg object accelerates at 2 m/s². What force is acting on it?
Solution — Step by Step
The relationship between force, mass, and acceleration is Newton’s Second Law:
Force equals mass multiplied by acceleration. This is the single most-used formula in mechanics — you’ll see it everywhere from Class 8 boards to JEE.
From the problem:
- Mass, kg
- Acceleration, m/s²
Both are in SI units already, so we don’t need any conversion.
The force acting on the object is 10 N.
Why This Works
Newton’s Second Law tells us that force is what causes acceleration. If you push harder (more force) on the same object, it accelerates more. If you push the same way on a heavier object, it accelerates less. The formula captures exactly this balance.
The unit Newton (N) is defined precisely as the force needed to accelerate 1 kg at 1 m/s². So when we write , the units work out automatically: .
This is why we use SI units throughout — mixing kg with cm/s² would give a wrong numerical answer. Always check units before substituting.
Alternative Method
We can approach this by thinking about what “force” physically means — a push or pull that changes the state of motion.
If the same 10 N force acted on a 10 kg object instead, the acceleration would be:
Half the acceleration for double the mass. This proportional reasoning is useful for comparison-type questions: “If mass is doubled and force is kept the same, what happens to acceleration?” Answer: acceleration halves. NCERT loves these.
Common Mistake
Writing the answer as 10 m/s² instead of 10 N.
Students sometimes forget to change the unit after calculating. The calculation gives , and since you just saw “m/s²” in the problem, the brain auto-fills that unit. But force is in Newtons (N), not m/s². Always write the unit explicitly — in board exams, the unit carries marks.
A quick sanity check: Force is always in N, acceleration in m/s², and mass in kg. If your answer for force has any other unit, something went wrong in the substitution.