Apply Newton's second law F = ma to calculate force. Simple numerical.

Calculate Force Given Mass and Acceleration — F = ma Problem

This is a standard NCERT-style numerical that tests the most fundamental application of Newton's Second Law. The twist here is that force isn't given directly — you have to find acceleration first from the velocity data, then apply $F = ma$ . Two-step problem. Students who miss the first step lose all marks.

Question

A body of mass 5 kg is moving with a velocity of 10 m/s. A force is applied for 2 seconds, after which the velocity becomes 20 m/s. Find the force applied.

Solution — Step by Step

Step 1: Find the acceleration.

We know initial velocity, final velocity, and time. Use the first equation of motion:

$a = \frac{v - u}{t}$

$a = \frac{20 - 10}{2} = \frac{10}{2} = 5 \text{ m/s}^2$

Step 2: Apply Newton's Second Law.

$F = ma$

$F = 5 \times 5 = 25 \text{ N}$

Answer: The force applied is 25 N.

Why This Works

Newton's Second Law connects force to the rate of change of velocity, not to velocity itself. The body is already moving at 10 m/s — that's not what matters. What matters is that the force caused the velocity to change by 10 m/s in 2 seconds. That change is what $F = ma$ captures.

Think of it this way: a constant 25 N force on a 5 kg body will always produce $5 \text{ m/s}^2$ of acceleration, regardless of whether the body starts at rest, at 10 m/s, or at 100 m/s.

📌 Note

The direction of the force is the same as the direction of acceleration. Since the body sped up (velocity increased in its direction of motion), the force acted in the direction of motion.

Alternative Method — Using Impulse-Momentum Theorem

We can also solve this using impulse, which is arguably more direct:

$F \cdot \Delta t = m(v - u)$

$F \times 2 = 5 \times (20 - 10)$

$F \times 2 = 50$

$F = 25 \text{ N}$

Same answer. The impulse-momentum approach is preferred when questions involve short-duration forces (like collisions) where acceleration might not be cleanly defined. For uniform-force problems like this one, both methods work equally well.

Common Mistake

⚠️ Common Mistake

The most frequent error: using $F = mv$ instead of $F = ma$ . Force is NOT mass times velocity. Force is mass times acceleration. Velocity is the state; acceleration is the change in that state. Writing $F = 5 \times 20 = 100$ N uses velocity instead of acceleration — this is a classic first-chapter mistake that gets hammered in MCQs.

A second mistake is treating velocity as acceleration. The body has velocity 10 m/s — that is not its acceleration. Acceleration $= \dfrac{\Delta v}{\Delta t} = \dfrac{20 - 10}{2} = 5$ m/s². These are different quantities with different units (m/s vs m/s²).

Question

Solution — Step by Step

Why This Works

Alternative Method — Using Impulse-Momentum Theorem

Common Mistake

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