O-Level Physics: Calculating Relative Velocity

Q: How do you calculate relative velocity of objects moving in the same direction?

Subtract the speeds. If Car A moves at 30 m/s and Car B moves ahead of it at 40 m/s, the relative velocity of B from A's perspective is 40 - 30 = 10 m/s moving away.

Q: How do you calculate relative velocity of objects moving in opposite directions?

Add the speeds. If you are driving at 20 m/s and a truck is driving towards you at 30 m/s, the truck approaches you at a relative speed of 50 m/s.

Q: What is a vector triangle used for?

A vector triangle is used to find the resultant velocity of an object moving in two dimensions, such as a boat crossing a river while being pushed sideways by a current.

Q: How do you draw a vector triangle correctly?

Draw the vectors 'tip-to-tail'. Start with the object's velocity, then draw the external velocity (like the wind or river) starting from the arrowhead of the first vector. The resultant velocity is drawn from the very start point to the very end point.

A vector triangle showing a boat crossing a river pushed by a current.

What is the rule for 1D relative velocity calculations?

If two objects are moving towards each other (or away from each other), ADD their speeds together. If one is chasing the other in the same direction, SUBTRACT the slower speed from the faster speed. In 2D space (like a plane in a crosswind), use Pythagoras' theorem and a vector triangle.

1. The 1D Highway Rule (Trains & Cars)
2. The 2D Vector Triangle (Boats & Planes)
3. Worked Exam Question (The Crosswind Trap)
4. Frequently Asked Questions

Most students understand how to calculate speed (distance/time). But when you put an object inside a moving environment — like a boat floating down a river, or a person running on a train — the calculations break down. This guide within our Ultimate O-Level Physics Guide decodes the vector triangle system used by CAIE examiners.

1. The 1D Highway Rule (Trains & Cars)

One-dimensional physics means everything is moving on a single straight line. There are only two scenarios:

Scenario A: Same Direction (Chasing)

Imagine you are driving at 30 m/s. The car in front of you is driving at 35 m/s. To you, it looks like they are slowly pulling away at 5 m/s.Rule: Subtract the speeds. (35 - 30 = 5 m/s).

Scenario B: Opposite Directions (Head-On/Diverging)

Imagine you are driving at 30 m/s past traffic going the other way. A truck comes towards you at 30 m/s. From your perspective, the truck whips past you at 60 m/s!Rule: Add the speeds. (30 + 30 = 60 m/s).

2. The 2D Vector Triangle (Boats & Planes)

CAIE Paper 2 loves asking about a boat crossing a river, or a plane flying through a crosswind. In these cases, the object is moving forward, but the environment is pushing it to the side.

You cannot simply add or subtract. You must draw a vector triangle scale diagram or use Pythagoras' Theorem.

💡 Tutor's Tip

Golden Rule of Vectors: Draw them tip-to-tail. Start the second arrow exactly where the arrowhead of the first arrow ends. Do not draw both arrows starting from the same central dot. That will give you the wrong diagonal.

3. Worked Exam Question (The Crosswind Trap)

Question:

An aircraft's engines drive it due North at a velocity of 80 m/s. A strong wind blows from West to East at a velocity of 60 m/s. Calculate the magnitude of the resultant velocity of the aircraft.

Step 1 — Identify the axes and draw

Vector 1 (Plane): 80 m/s North (straight up).
Vector 2 (Wind): 60 m/s East (straight right).
Since they are North and East, they meet at a perfect 90° angle. We have a right-angled triangle.

Step 2 — Use Pythagoras

The resultant velocity is the hypotenuse (the diagonal from start to finish).

c² = a² + b²
c² = 80² + 60²
c² = 6400 + 3600 = 10000
c = √10000 = 100 m/s

📋 From the Desk of David Chen

Half the students I examine forget to read the second part of this question, which always asks: "Calculate the angle of the resultant velocity." You need to use trigonometry (SOH CAH TOA) to find the angle of the triangle you just drew. Here, tan(θ) = 60/80 = 0.75. Then take inverse tan (tan⁻¹(0.75)) to find the angle is 36.9° East of North!

Frequently Asked Questions

How do you calculate relative velocity of objects moving in the same direction?▼

Subtract the speeds. If Car A is at 40 m/s and Car B is at 30 m/s ahead of it, A is catching up to B at a relative speed of 10 m/s.

How do you calculate relative velocity of objects moving in opposite directions?▼

Add the speeds. If two cars drive toward each other at 50 m/s each, they approach each other at 100 m/s.

What is a vector triangle used for?▼

It calculates the resultant (final) velocity of an object that is subjected to two perpendicular movements, like an airplane in a crosswind.

How do you draw a vector triangle correctly?▼

Always draw the vectors 'tip-to-tail'. The resultant vector is the line that connects the very starting point to the very end point.

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Relative Velocity: Mastering 1D Trains and 2D Boats