(d) Relative motion practice problems

Q1. Car Chase

Two cars travel on a straight road.

Car A moves at 20 m/s, and Car B follows at 30 m/s.

(a) What is the velocity of Car B relative to Car A?

(b) If they are 200 m apart, how long will it take Car B to catch up?

ANSWERS to relative motion questions

Q2. Passenger Perspective

A train moves east at 15 m/s.

A passenger walks west along the aisle at 2 m/s.

(a) What is the passenger’s velocity relative to the ground?

(b) What is the passenger’s velocity relative to another seated passenger?

ANSWERS to relative motion questions

Q3. Opposing Cyclists

Cyclist A travels north at 5 m/s. Cyclist B moves south at 7 m/s.

(a) What is the velocity of B relative to A?

(b) How does this change if they were both moving north instead?

ANSWERS to relative motion questions

Q4. Relative Displacement

Two runners start from the same point.

Runner X moves at 4 m/s.

Runner Y moves at 3 m/s in the same direction.

(a) What is Y’s displacement relative to X after 60 seconds?

(b) If X turns around and runs towards Y at the same speed, how long until they meet?

ANSWERS to relative motion questions

(e) Relative Motion in Real Life

Overtaking on the Motorway

• You’re driving at 60 mph and a car overtakes you at 70 mph - the relative velocity is 10 mph.
• You perceive that car as moving “faster than you” even though both are moving forward.

Walking on a Train

• You walk toward the front of a train going 30 km/h. If you walk at 5 km/h, your velocity relative to the ground = 35 km/h.
• If you walk backwards, your velocity relative to the ground = 25 km/h.

Headwinds versus Tailwinds

• A cyclist moving at 20 km/h against a 5 km/h wind feels like they're moving slower (relative motion).
• With a tailwind, the motion feels easier - same principle at play.

Key points about speed and velocity - interpreting distance-time graphs

Information sources for Doc Brown's key points: IGCSE-GCSE physics are based on textbooks & syllabus-specifications for students taking the UK AQA, Edexcel, OCR 21st Century Science, OCR Gateway science suite, WJEC, CCEA and CIE GCSE physics 9-1 level science examinations

A set of GCSE/IGCSE-style practice problems on relative motion, designed to mirror the kinds of questions you might see across WJEC, CCEA, CIE, AQA, Edexcel, and OCR specifications. I’ve included varied formats to target conceptual understanding, calculations, and graphical interpretation.

Relative Motion of Two Objects

Core Concept

• Relative motion describes how the motion of one object appears from the perspective of another moving object.
• It depends on the frame of reference - the observer’s position and motion.

Key Definitions

• Velocity: Speed in a given direction (vector).
• Relative velocity: The velocity of one object as observed from another moving object.

Equations

• If two objects move in the same direction: subtract one velocity from the other
• If two objects move in opposite directions: add the two velocities together
• Displacement and time remain consistent across frames if measured simultaneously.

Conceptual Examples

• A passenger walking forward in a train moving at 10 m/s: their velocity relative to the ground is the sum of walking speed and train speed.
• Two cars moving in opposite directions at 20 m/s and 30 m/s: relative velocity = 50 m/s.

Graphical Interpretation

• Distance-time graphs: Show how far one object is from another over time.
• Velocity-time graphs: Can be used to compare velocities and deduce relative motion.

  See sections

  1.1 Technical terms explained, examples of speeds quoted, speed formula

  1.2 Speed, distance and time calculations - problem solving

  1.3 Drawing and interpreting distance-time graphs, calculations, problems

Typical Exam Board Syllabus Content

Student Exam Tips

• Always define your frame of reference before solving relative motion problems.
• Use vector diagrams to visualize direction and magnitude.
• Practice with velocity-time graphs to interpret acceleration and relative speed.
• Think conceptually: relative motion is about how one object perceives another.
• Use worked examples to reinforce understanding - especially in collision or pursuit scenarios.

Keywords, phrases and learning objectives for speed, motion and graphs

Know what is meant by the relative motion of two moving object.

Be able to calculate relative speed of two objects whether they are travelling in the same direction or opposite directions.

SITEMAP Website content © Dr Phil Brown 2000+. All copyrights reserved on Doc Brown's physics revision notes, images, quizzes, worksheets etc. Copying of website material is NOT permitted. Exam revision summaries and references to GCSE science course specifications are unofficial.

INDEX physics notes: Speed calculations and distance-time graphs

ANSWERS to relative motion questions

Q1. Car Chase

Two cars travel on a straight road.

Car A moves at 20 m/s, and Car B follows at 30 m/s.

(a) What is the velocity of Car B relative to Car A?

30 - 20 = 10 m/s faster

(b) If they are 200 m apart, how long will it take Car B to catch up?

v = d / t, so t = d / v = 200 / 10 = 20 seconds

Q2. Passenger Perspective

A train moves east at 15 m/s.

A passenger walks west along the aisle at 2 m/s.

(a) What is the passenger’s velocity relative to the ground?

15 - 2 = 13 m/s in an easterly direction

(b) What is the passenger’s velocity relative to another seated passenger?

2 m/s  in an easterly direction, seated passenger's velocity is zero.

Q3. Opposing Cyclists

Cyclist A travels north at 5 m/s. Cyclist B moves south at 7 m/s.

(a) What is the velocity of B relative to A?

5 + 7 = 12 m/s in south direction

(b) How does this change if they were both moving north instead?

Cyclist B is faster than cyclist A by 2 m/s in a north direction.

Q4. Relative Displacement

Two runners start from the same point.

Runner X moves at 4 m/s.

Runner Y moves at 3 m/s in the same direction.

(a) What is Y’s displacement relative to X after 60 seconds?

4-1 = 3, means runner X is moving 1 m/s faster than runner Y

v = d / t, so d = vt = 1 x 60 = 60 m ahead of runner Y for runner X

(or runner Y is 60 m behind runner X)

(b) If X turns around and runs towards Y at the same speed, how long until they meet?

This means runner X is running towards Y at a relative velocity of 4 + 3 = 7 m/s

v = d / t, t = d / v = 60 / 7 = ~8.6 s

INDEX physics notes: Speed calculations and distance-time graphs