Second Law of Motion More force, more speed—see the connection.

Key Idea

Newton’s Second Law

An object accelerates more when the net force is larger and less when its mass is bigger.

Shopping Cart Story

1

Empty Cart

Small mass, gentle push—cart accelerates easily.

2

Loaded Cart

Big mass needs stronger push for the same acceleration.

3

Double Push

Twice the force makes the cart speed up faster.

Pro Tip:

Second Law: more force gives more acceleration, but more mass cuts it down.

The Equation

\[F = m \times a\]

Variable Definitions

F Net force (Newtons)
m Mass (kilograms)
a Acceleration (m/s2)

Applications

Solve for force

Multiply mass by acceleration to find net force.

Check units

Use kg for m and m/s² for a so F is in Newtons.

Force vs Acceleration

Force vs Acceleration graph for a 2 kg cart

Force vs Acceleration graph for a 2 kg cart

Straight line means direct proportion

The straight line through the origin is a graphical representation of Force (N) against Acceleration (m/s²).

Because the line is straight, doubling acceleration doubles force—showing a direct proportion \(F \propto a\).

Key Points:

  • Slope of line = mass = 2 kg.
  • Line passes origin, so zero force at zero acceleration.
  • Any point confirms \(F = ma\).

Quick Check

Question

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

1
2 m/s²
2
5 m/s²
3
10 m/s²
4
20 m/s²

Hint:

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

Lesson Recap

Acceleration Factors

Changes with applied force and the object’s mass.

Core Formula

\(F = m \times a\) links force, mass, and acceleration.

More Force

Stronger push gives faster acceleration.

More Mass

Heavier objects accelerate less under the same force.

Daily Examples

Cart pushes, bike rides, and football kicks show the law.