Speed, Distance and Time: KS3 Physics Guide

Speed is the distance an object travels per unit of time. The formula is: speed = distance ÷ time. In SI units, speed is measured in metres per second (m/s), distance in metres (m), and time in seconds (s). This relationship — and how to rearrange it — is one of the most assessed calculation topics in KS3 physics.

The speed, distance and time formula

The three quantities are linked by one equation:

speed = distance ÷ time

Written with symbols:

v = d ÷ t (or v = d/t)

where:

• v = speed (m/s or km/h depending on the units given)
• d = distance (m or km)
• t = time (s or h)

The formula triangle

Many students find the formula triangle a useful memory aid. Draw a triangle divided into three sections:

       [ d ]
      -------
     [ v | t ]

Cover the quantity you want to find with your finger:

• Cover d → what remains is v × t → so d = v × t
• Cover v → what remains is d ÷ t → so v = d ÷ t
• Cover t → what remains is d ÷ v → so t = d ÷ v

The triangle gives you the three rearrangements without having to manipulate algebra, which is handy under exam pressure. However, you should also practise the algebra directly, as GCSE mark schemes often require you to show the rearrangement as working.

Units matter: be consistent

The most common error in KS3 and GCSE speed calculations is mixing units. Check every question:

If a question gives distance in km and time in seconds, convert first before substituting into the formula. Always state your units in the final answer — marks are commonly lost for missing units.

Worked example 1: finding speed

Question: A cyclist travels 1,200 m in 4 minutes. What is their average speed in m/s?

Step 1: Convert time to seconds.
4 minutes × 60 = 240 seconds

Step 2: Write the formula.
v = d ÷ t

Step 3: Substitute values.
v = 1,200 ÷ 240

Step 4: Calculate.
v = 5 m/s

Answer: The cyclist's average speed is 5 m/s.

Worked example 2: finding distance

Question: A train travels at an average speed of 90 km/h for 2.5 hours. How far does it travel?

Step 1: Write the rearranged formula.
d = v × t

Step 2: Substitute values.
d = 90 × 2.5

Step 3: Calculate.
d = 225 km

Answer: The train travels 225 km.

Worked example 3: finding time

Question: A runner completes a 10,000 m race at an average speed of 4 m/s. How long does the race take? Give your answer in minutes.

Step 1: Write the rearranged formula.
t = d ÷ v

Step 2: Substitute values.
t = 10,000 ÷ 4

Step 3: Calculate.
t = 2,500 seconds

Step 4: Convert to minutes.
2,500 ÷ 60 = 41.7 minutes (to 1 decimal place)

Answer: The race takes approximately 41.7 minutes.

Average speed versus instantaneous speed

An important distinction at KS3 and GCSE:

Average speed is the total distance divided by the total time for a journey. A car journey of 120 km taking 2 hours has an average speed of 60 km/h, even though the car stopped at traffic lights, accelerated, and braked throughout.

Instantaneous speed is the speed at one specific moment in time — what a speedometer reads. It can be higher or lower than the average speed at any point in the journey.

Most KS3 exam questions use average speed unless they specifically say "at that moment" or show a single point on a distance-time graph.

Reading distance-time graphs

Distance-time graphs are a core KS3 physics skill assessed alongside the formula.

• A horizontal line means the object is stationary (not moving) — distance is not changing with time.
• A straight diagonal line means the object moves at constant speed — the gradient equals the speed.
• A steeper gradient means a higher speed.
• A curve getting steeper means the object is accelerating (speed increasing over time).

To find speed from a distance-time graph: choose two points on the straight line, read off their coordinates, and calculate:

speed = change in distance ÷ change in time = rise ÷ run

This is the gradient of the line. At KS3, you will typically work with straight sections; curved sections (acceleration) are more commonly assessed at GCSE.

Common exam errors

Error 1: Forgetting to convert minutes to seconds If time is given in minutes, multiply by 60 before using the formula (when distance is in metres).

Error 2: Missing units Always write m/s, km/h, or whatever unit is appropriate. A numerical answer without units will lose the unit mark.

Error 3: Confusing distance and displacement Distance is the total path length travelled (a scalar — it has magnitude only). Displacement is the straight-line distance from start to finish in a specific direction (a vector — it has magnitude AND direction). Speed uses distance; velocity uses displacement. At KS3 the distinction is introduced; it is more heavily assessed at GCSE.

Error 4: Using the wrong units for the same calculation If distance is in km and time is in seconds, the result will be in km/s — which is extremely fast (faster than most rockets). Check your answer is plausible before writing it down.

What does the national curriculum say?

The Department for Education's Science Programmes of Study for Key Stage 3 requires pupils to learn "speed and the quantitative relationship between average speed, distance and time" and to "calculate speeds." BBC Bitesize KS3 physics covers the formula, the triangle, worked examples, and distance-time graphs as core content for this topic.

Frequently asked questions

What is the formula for speed at KS3?

Speed = distance ÷ time, or v = d/t. You also need to know the two rearrangements: distance = speed × time (d = v × t) and time = distance ÷ speed (t = d/v).

What units is speed measured in?

In SI units, speed is measured in metres per second (m/s). In everyday contexts, kilometres per hour (km/h) or miles per hour (mph) are used. Always check which units a question is using and convert where needed before calculating.

How do you use the formula triangle for speed?

Draw a triangle with d at the top and v and t at the bottom. Cover the quantity you want to find: cover d to get v × t; cover v to get d ÷ t; cover t to get d ÷ v. The triangle gives all three versions of the formula without rearranging.

What does the gradient of a distance-time graph represent?

The gradient (steepness) of a distance-time graph represents speed. A steeper gradient means a higher speed. A horizontal line means the object is stationary. Use gradient = rise ÷ run = change in distance ÷ change in time to calculate the speed from a graph.

What is the difference between speed and velocity?

Speed is a scalar — it tells you how fast an object is moving (magnitude only). Velocity is a vector — it tells you both how fast and in which direction. A car going 60 km/h north and a car going 60 km/h south have the same speed but different velocities. At KS3 this distinction is introduced; it is more extensively covered at GCSE.

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