Relative Motion Practice Test Worksheets
Relative motion questions test whether you can decide when speeds should be added, when they should be subtracted, and how a delayed start changes the remaining gap. This page shows the main patterns with worked examples.
For students who can use speed, distance, and time, but get stuck when two moving objects have to be compared.
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What Do Relative Motion Questions Look Like?
Relative motion questions give you the speeds, starting positions, and start times of two moving people or vehicles. You are asked to determine when they will meet or catch up, what closing speed applies, or what distance each traveller covers. Here is a worked example.
Two Walkers Moving Towards Each Other
Question: Hugo and Ines start walking towards each other along a path that is 32 miles long. Hugo walks at 5 mph. Ines walks at 3 mph. They start at the same time and travel at constant speeds until they meet.
(a) What is the combined speed of both walkers?
(b) At the moment they meet, how far has each walker gone?
Worked Method
Step 1: They are moving towards each other, so add their speeds: 5 + 3 = 8 mph.
Step 2: Time to meet = 32 ÷ 8 = 4 hours.
Step 3: Hugo travels 5 × 4 = 20 miles. Ines travels 3 × 4 = 12 miles.
Tip: Check the two distances add to the original gap: 20 + 12 = 32 miles.
Rules to Help You Solve Relative Motion Questions
Most questions in the pack are built from the same speed, distance, and time relationships. Using the approach from the example above, the key is deciding which speed closes the gap.
↔ Rule 1: Moving towards each other means add speeds
When two people or vehicles travel towards each other, the gap closes at their combined speed.
Example: 5 mph and 3 mph towards each other gives a closing speed of 8 mph.
⏱ Rule 2: Time = gap ÷ closing speed
For a constant, positive closing speed, divide the gap by that speed to find the time to meet. Use matching units: miles divided by miles per hour gives hours.
Example: A 32 mile gap closing at 8 mph takes 32 ÷ 8 = 4 hours.
🏁 Rule 3: Catch-up questions use the speed difference
When a faster traveller starts behind a slower traveller moving in the same direction, the gap closes at the faster speed minus the slower speed. At equal constant speeds the gap stays unchanged; if the traveller behind is slower, the gap grows.
Example: 40 mph chasing 25 mph closes the gap at 40 - 25 = 15 mph.
⌛ Rule 4: Delays change the starting gap
First find the early traveller’s distance: speed × delay. If they move towards the waiting traveller, subtract that distance from the original gap. In a chase from the same starting point, it becomes the early traveller’s head start. Then use the appropriate closing speed for the remaining gap, provided they have not already met.
Example: Travelling towards someone waiting 210 miles away at 50 mph for 1 hour reduces the gap by 50 miles, leaving 160 miles.
Two More Worked Examples
Here are two additional problems showing how to account for delayed start times and how to calculate catch-up distance when vehicles travel in the same direction.
One Traveller Starts Later
Question: Jenny and Sunil are 210 miles apart. Jenny starts travelling towards Sunil at 50 mph. 1 hour later, Sunil starts travelling towards Jenny at 30 mph.
(a) What distance remains between them when Sunil starts travelling?
(b) What is the distance covered by Sunil?
Worked Method
Step 1: Jenny travels for 1 hour before Sunil starts, so she covers 50 × 1 = 50 miles.
Step 2: Remaining gap = 210 - 50 = 160 miles.
Step 3: Once both are moving, their combined speed is 50 + 30 = 80 mph.
Step 4: Time after Sunil starts = 160 ÷ 80 = 2 hours, so Sunil travels 30 × 2 = 60 miles.
Tip: Do the delay first. The original gap is no longer the gap once both people are moving.
Catching a Slower Vehicle
Question: A car is 60 miles ahead of a motorcycle on a highway. The car travels at 25 mph. The motorcycle chases it at 40 mph.
(a) By how much does one speed exceed the other?
(b) What total distance does the motorcycle cover to catch up?
Worked Method
Step 1: Both are travelling in the same direction, so use the speed difference: 40 - 25 = 15 mph.
Step 2: Time to catch up = 60 ÷ 15 = 4 hours.
Step 3: Motorcycle distance = 40 × 4 = 160 miles.
Tip: For travellers moving towards each other, add their speeds to find the closing speed. For a faster traveller catching a slower one ahead, subtract the slower speed from the faster speed.
