What is the difference between mass and weight?

Mass is the amount of matter in an object (kg) and stays constant everywhere. Weight is the gravitational force on that mass (W = mg). On Earth g ≈ 9.81 m/s²; on the Moon g ≈ 1.62 m/s², so the same mass weighs about 6× less.

What is Newton's First Law?

An object remains at rest or in uniform motion unless acted upon by a net external force. This is the law of inertia — it explains why you feel pushed back when a car accelerates.

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. A rocket engine pushes exhaust downward; the exhaust pushes the rocket upward.

How do I convert between km/h and m/s?

Multiply km/h by 1000/3600 = 1/3.6. Example: 100 km/h = 100/3.6 = 27.78 m/s. To convert m/s to km/h, multiply by 3.6.

Formula Guide

How to Calculate Force, Acceleration & Motion (Newton's Laws)

Newton's three laws of motion describe how forces affect objects. The second law — F = ma — is the most used in calculations: force equals mass times acceleration. Combined with kinematics equations (motion under constant acceleration), you can calculate velocity, distance, and time for any object in motion. These principles apply from a car braking to a rocket launching.

Last updated: March 31, 2026

The Formula

Newton's 2nd Law:  F = m × a
Acceleration:      a = F / m
Kinematics (constant acceleration):
  v = u + at
  s = ut + ½at²
  v² = u² + 2as
Momentum:          p = m × v
Impulse:           J = F × t = Δp

Units: Force (F) in Newtons (N = kg·m/s²), Mass (m) in kg, Acceleration (a) in m/s², Velocity (v, u) in m/s, Distance (s) in metres.

Variable Definitions

Symbol	Name	Description
F	Force	The push or pull acting on an object, in Newtons (N)
m	Mass	The amount of matter in an object, in kilograms (kg)
a	Acceleration	Rate of change of velocity, in m/s²
u, v	Initial / Final Velocity	u = velocity at the start, v = velocity at the end of the time interval (m/s)
s	Displacement	Distance travelled in a given direction, in metres

Step-by-Step Example

A 1,200 kg car accelerates from rest (0 m/s) to 27.8 m/s (100 km/h) in 8 seconds. Find the acceleration, force, and distance covered.

Given

Mass (m):1,200 kgInitial velocity (u):0 m/sFinal velocity (v):27.8 m/sTime (t):8 s

Solution

1
Calculate acceleration: a = (v − u) / t: a = (27.8 − 0) / 8 = 3.475 m/s²
2
Calculate force: F = m × a: F = 1200 × 3.475 = 4,170 N
3
Calculate distance: s = ut + ½at²: s = 0×8 + ½×3.475×64 = 111.2 m

Acceleration = 3.48 m/s², Force = 4,170 N, Distance = 111.2 m.

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Common Mistakes to Avoid

Confusing mass and weight — mass is kg, weight is the force of gravity (W = mg). On Earth g ≈ 9.81 m/s².

Using the wrong kinematics equation — check which of u, v, a, s, t you know and which you need to find; pick the equation that contains exactly those variables.

Ignoring the direction of force — Newton's laws are vector equations; forces in opposite directions must be subtracted.

Forgetting friction or air resistance — real-world force calculations must account for opposing forces unless told to ignore them.

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