Second Law of Motion Force meets mass—watch acceleration come alive!

Law in Simple Words

Newton’s Second Law

Push harder and an object speeds up more. If the object is heavier, it speeds up less with the same push.

Which will speed up more with the same push: a loaded shopping cart or an empty one?

The Equation

\[F = m \times a\]

Variable Definitions

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

Know any two variables to find the third.

Applications

Finding Force

Compute push required to speed up a trolley.

Finding Mass

Estimate mass when force and acceleration are known.

Finding Acceleration

Predict how fast a scooter speeds up under a given force.

Cause & Effect

Relationship examples—see how force or mass changes acceleration.

  1. 1

    Double the force

    Mass same ⇒ acceleration doubles.

  2. 2

    Double the mass

    Force same ⇒ acceleration halves.

  3. 3

    No net force

    Acceleration is zero; speed and direction stay same.

Remember: \(a = \frac{F}{m}\) — direct with force, inverse with mass.

Multiple Choice Question

Question

A 4 kg cart is pushed with 12 N. Using \(F = m a\), what is its acceleration?

1
0.3 m/s²
2
3 m/s²
3
48 m/s²
4
16 m/s²

Hint:

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

Key Points

Stronger push, faster change

More applied force gives greater acceleration.

Heavier mass, slower change

A larger mass accelerates less under the same force.

Formula link

Newton summed it up: \(F = m \times a\).

Direct & inverse relations

Acceleration grows with force and shrinks with mass.