Basic Physics Laws for Students: Newton, Energy, and Motion Explained

Q: What does F = ma mean?

F = ma is Newton's Second Law. Force (F) equals mass (m) times acceleration (a). It means a larger force produces more acceleration, and a heavier object needs more force to accelerate at the same rate.

Q: What is Newton's Third Law?

Newton's Third Law states that for every action there is an equal and opposite reaction. When you push on a wall, the wall pushes back on you with the same force in the opposite direction.

Q: What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another. The total energy in a closed system always remains constant.

Q: What is the difference between speed and velocity?

Speed is a scalar quantity — it tells you how fast an object moves (magnitude only). Velocity is a vector quantity — it tells you both how fast and in what direction. A car going 60 mph has a speed of 60 mph, but its velocity is 60 mph north (or some specific direction).

Science › Physics | Tutorial with worked examples | Grades 7–10

Learning Objectives By the end of this tutorial you will be able to: state and apply Newton’s three laws of motion; use F = ma to calculate force, mass, or acceleration; distinguish between speed and velocity; explain kinetic and potential energy; apply the law of conservation of energy to everyday scenarios.

Physics can feel intimidating, but at its core it is the science of how things move and interact. The fundamental laws discovered over the past 400 years explain everything from why a basketball bounces to how rockets reach orbit. This tutorial walks through the big ideas step by step, with worked problems you can use as models.

1. What Is a Physical Law?

A physical law is a statement, usually expressed mathematically, that describes a pattern observed consistently in nature. Unlike a hypothesis or a theory, a law does not attempt to explain why the pattern exists—it simply describes what always happens under given conditions. Isaac Newton’s laws of motion (published 1687) remain some of the most powerful tools in all of science.

2. Key Vocabulary Before We Begin

Force — a push or pull that can change an object’s motion. Measured in Newtons (N).
Mass — the amount of matter in an object. Measured in kilograms (kg). Mass does not change with location.
Weight — the gravitational force on an object = mass × g (where g ≈ 9.8 m/s² on Earth). Weight changes with location.
Speed — distance traveled per unit time (scalar: magnitude only).
Velocity — speed in a specific direction (vector: magnitude + direction).
Acceleration — rate of change of velocity (can be speeding up, slowing down, or changing direction).
Inertia — the tendency of an object to resist changes in its state of motion.

3. Newton’s First Law — The Law of Inertia

“An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by an unbalanced external force.”

This tells us that objects do not change their motion on their own. A hockey puck slides until friction (an unbalanced force) slows it. A satellite orbiting in the vacuum of space keeps moving because almost nothing acts on it to slow it down.

Worked Example 3-A: Identifying Balanced vs. Unbalanced Forces A book sits motionless on a table. Is it in equilibrium? Forces acting on the book: • Gravity pulling down: 10 N (downward) • Normal force from table: 10 N (upward) Net force = 10 N − 10 N = 0 N Because the net force is zero, forces are BALANCED. The book stays at rest. → First Law confirmed.

Worked Example 3-B: Inertia in a Car A passenger is riding in a car traveling at 60 km/h. The driver brakes suddenly (an external force on the car). The passenger’s body has inertia → it tends to keep moving at 60 km/h. Without a seatbelt, the passenger leans sharply forward. The seatbelt provides the unbalanced force to decelerate the passenger at the same rate as the car. This is First Law in everyday life.

4. Newton’s Second Law — F = ma

The second law quantifies how forces produce acceleration:

Force = Mass × Acceleration (F = ma)

Units: if mass is in kg and acceleration in m/s², then force is in Newtons (N). Rearranged: a = F/m and m = F/a.

Key insight: for the same force, a heavier object accelerates less. For the same mass, a larger force produces more acceleration.

Worked Example 4-A: Finding Acceleration A 5 kg cart is pushed with a net force of 20 N. What is its acceleration? Formula: a = F ÷ m a = 20 N ÷ 5 kg a = 4 m/s² The cart accelerates at 4 metres per second squared.

Worked Example 4-B: Finding Force A 70 kg sprinter accelerates at 3 m/s² off the starting blocks. What net force is required? Formula: F = m × a F = 70 kg × 3 m/s² F = 210 N The sprinter’s muscles (and ground reaction) must produce 210 N of net force.

Worked Example 4-C: Finding Mass A force of 150 N produces an acceleration of 5 m/s². What is the mass of the object? Formula: m = F ÷ a m = 150 N ÷ 5 m/s² m = 30 kg

5. Newton’s Third Law — Action and Reaction

“For every action there is an equal and opposite reaction.”

Forces always come in pairs. When object A exerts a force on object B, object B exerts an equal force in the opposite direction on object A. These forces act on different objects, which is why they do not cancel each other out.

Worked Example 5-A: Rocket Propulsion A rocket engine expels exhaust gases downward at high speed. ACTION: engine pushes exhaust gases downward. REACTION: exhaust gases push rocket upward. The two forces are equal in magnitude and opposite in direction. The rocket lifts off because the reaction force overcomes gravity.

Worked Example 5-B: Walking Your foot pushes backward on the ground (action). The ground pushes your foot forward (reaction). This forward reaction force propels you forward. Without friction (e.g., on ice), the ground cannot push back effectively → you slip.

6. Speed, Velocity, and Acceleration

These three concepts are often confused. Here is how they connect:

Speed (scalar): speed = distance ÷ time • e.g., 30 m/s
Velocity (vector): velocity = displacement ÷ time, in a specific direction • e.g., 30 m/s due north
Acceleration: a = (final velocity − initial velocity) ÷ time • e.g., 3 m/s²

Worked Example 6-A: Calculating Average Speed A cyclist rides 120 metres in 8 seconds. Speed = distance ÷ time Speed = 120 m ÷ 8 s Speed = 15 m/s

Worked Example 6-B: Calculating Acceleration A car speeds up from 10 m/s to 25 m/s in 5 seconds. a = (v_final − v_initial) ÷ time a = (25 − 10) m/s ÷ 5 s a = 15 m/s ÷ 5 s a = 3 m/s²

7. Kinetic and Potential Energy

Kinetic energy (KE) is the energy of motion. Any moving object has kinetic energy:

KE = ½ × m × v²

Potential energy (PE) is stored energy due to position or condition. Gravitational PE depends on height:

PE = m × g × h

where g ≈ 9.8 m/s² and h is height in metres above the reference point.

Worked Example 7-A: Kinetic Energy A 2 kg ball rolls at 6 m/s. KE = ½ × m × v² KE = ½ × 2 kg × (6 m/s)² KE = ½ × 2 × 36 KE = 36 Joules (J)

Worked Example 7-B: Potential Energy A 3 kg book sits on a shelf 2 metres above the floor. PE = m × g × h PE = 3 kg × 9.8 m/s² × 2 m PE = 58.8 Joules

8. Law of Conservation of Energy

Energy cannot be created or destroyed; it can only be converted from one form to another. In a system with no friction, the total mechanical energy (KE + PE) remains constant.

Worked Example 8: Rollercoaster Energy Conversion A rollercoaster car (mass 500 kg) starts from rest at the top of a 20 m hill. Ignoring friction, how fast is it moving at the bottom? At the top: KE = 0 (at rest), PE = mgh = 500 × 9.8 × 20 = 98,000 J At the bottom: PE = 0 (h = 0), KE = 98,000 J (all PE converted to KE) KE = ½mv² 98,000 = ½ × 500 × v² 98,000 = 250 v² v² = 392 v = √392 ≈ 19.8 m/s The car reaches approximately 19.8 m/s at the bottom.

9. Practice Problems

A 10 kg box accelerates at 2 m/s². What is the net force on the box?
A force of 60 N is applied to a 15 kg shopping trolley. What is its acceleration?
A 4 kg object is held 5 metres above the ground. What is its gravitational PE?
A skater moves at 8 m/s and has a mass of 60 kg. What is her kinetic energy?
A ball is dropped from a height where its PE is 200 J. What is its KE just before it hits the ground (ignore air resistance)?

Answers: 1) 20 N 2) 4 m/s² 3) 196 J 4) 1,920 J 5) 200 J (all PE converts to KE)

Frequently Asked Questions

What is Newton’s First Law of Motion? Newton’s First Law states that an object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by an unbalanced external force. This is also called the law of inertia.

What does F = ma mean? F = ma is Newton’s Second Law. Force equals mass times acceleration. A larger force produces more acceleration, and a heavier object needs more force to achieve the same acceleration.

What is Newton’s Third Law? For every action there is an equal and opposite reaction. When you push on a wall, the wall pushes back on you with the same force in the opposite direction.

What is the law of conservation of energy? Energy cannot be created or destroyed, only converted from one form to another. The total energy in a closed system always remains constant.

What is the difference between speed and velocity? Speed is a scalar quantity (magnitude only). Velocity is a vector quantity (magnitude + direction). A car doing 60 mph has a speed of 60 mph; its velocity is 60 mph in a specified direction.