Push, Mass & Zoom! More push or less mass makes motion dash!

Newton’s 2nd Law

Law Statement

Acceleration of an object depends directly on the applied force and inversely on its mass. Stronger push speeds it up; heavier load slows acceleration.

Think-pair-share: What happens if force and mass increase at the same time?

The Magic Equation

\[F = m \times a\]

Variable Definitions

F Force (newton, N)
m Mass (kilogram, kg)
a Acceleration (m/s²)

Applications

Rocket launch

Engines expel gas; large mass still accelerates upward.

Car braking

Brakes apply force to cut the car’s forward acceleration.

Throwing a ball

Greater force on the ball gives it higher acceleration.

Force vs Acceleration

https://asset.sparkl.ac/pb/sparkl-vector-images/img_ncert/93vVWBOBy2niFTTnBgctXhZjywwXFSmaOjahBNMO.png

Straight-line graph of force vs acceleration (m = 1 kg)

Direct Proportion: \(a \propto F\)

The graph plots force on the x-axis and acceleration on the y-axis.

A 1 N push gives 1 m/s²; 2 N gives 2 m/s². The straight line through the origin shows a constant slope.

Key Points:

  • Mass is fixed at 1 kg.
  • Slope of line = \( \frac{1}{m} = 1\;\text{kg}^{-1} \).

Worked Example

A force of 10 N acts on a 2 kg box. Find its acceleration.

  1. 1

    Write formula

    \(F = m \times a\)

  2. 2

    Rearrange

    \(a = \frac{F}{m}\)

  3. 3

    Substitute numbers

    \(a = \frac{10\ \text{N}}{2\ \text{kg}}\)

  4. 4

    Solve

    \(a = 5\ \text{m/s}^2\)

Tip: Always keep units with every number.

Multiple Choice Question

Question

If the force on an object is doubled while its mass stays the same, what happens to its acceleration?

1
It doubles
2
It halves
3
It stays the same
4
It becomes zero

Hint:

Look back at the straight line graph.

Key Takeaways

Remember these points

💪

More Force ➜ More Speed-up

Push harder and the object accelerates faster.

🏋️

More Mass ➜ Less Speed-up

Heavier objects need a bigger push.

🧮

Equation \(F = m \times a\)

A simple multiplication links the three quantities.

📊

Straight-Line Graph

Force vs acceleration is a straight line through origin when mass is constant.