Calculating Speed, Distance, and Time

Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took. The formula for speed is speed = distance ÷ time.

Speed Distance Time Triangle

Here we will learn about the speed distance time triangle including how they relate to each other, how to calculate each one and how to solve problems involving them.

There are also speed distance time triangle worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is speed distance time?

Speed distance time is the formula used to explain the relationship between speed, distance and time. That is:

Speed = Distance ÷ Time
Time = Distance ÷ Speed
Distance = Speed × Time

Or to put it another way distance divided by speed will give you the time. Provided you know two of the inputs you can work out the third.

For example if a car travels for 2 hours and covers 120 miles we can work out speed as 120 ÷ 2 = 60 miles per hour.

The units of the the distance and time tell you the units for the speed.

Example

Calculating Speed, Distance, and Time

Speed, distance, and time are fundamental concepts in physics that describe the motion of an object. The relationship between these three quantities is described by a simple equation, which allows you to calculate one of the variables if you know the other two.

The general approach to calculating speed, distance, and time involves:

Identifying the known values (speed, distance, or time).
Using the formula to calculate the unknown value.

Speed, Distance, and Time Formula

The fundamental equation for speed, distance, and time is:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Where:

Distance is the total distance traveled (in meters, m, or kilometers, km).
Speed is the rate at which an object moves (in meters per second, m/s, or kilometers per hour, km/h).
Time is the duration of travel (in seconds, s, or hours, h).

Example:

If a car travels at a constant speed of 60 km/h for 2 hours, we can calculate the distance traveled as:

Step 1: Use the formula: \( \text{Distance} = \text{Speed} \times \text{Time} \).
Step 2: Substitute the known values: \( \text{Distance} = 60 \, \text{km/h} \times 2 \, \text{h} \).
Step 3: Calculate the result: \( \text{Distance} = 120 \, \text{km} \).

Factors Affecting Speed, Distance, and Time

Several factors can affect the calculation of speed, distance, and time, including:

Speed: The speed can vary depending on conditions like traffic, terrain, or weather.
Time: The time taken can change if the object accelerates, decelerates, or stops for any reason.
Distance: The distance will change depending on the route taken or if there are any detours.

Real-life Applications of Speed, Distance, and Time Calculations

Calculating speed, distance, and time is essential in many practical situations, such as:

Travel planning, including calculating travel time for road trips, flights, and public transport.
Sports and athletics, such as determining the speed of a runner or a vehicle.
Engineering, especially in designing systems where speed and timing are critical, such as in robotics or conveyor belts.

Common Units for Speed, Distance, and Time

SI Units:

Speed: Meters per second (m/s) or kilometers per hour (km/h)
Distance: Meters (m) or kilometers (km)
Time: Seconds (s) or hours (h)

Understanding the relationship between speed, distance, and time is fundamental for solving motion-related problems and is widely used in fields such as transportation, physics, and engineering.

Common Operations with Speed, Distance, and Time

Solving for Unknown Variables: If you know two of the quantities (speed, distance, or time), you can solve for the third using the formula. For example, to solve for speed, use \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \), and to solve for time, use \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \).

Effect of Different Units: Ensure that the units for speed, distance, and time are consistent. If necessary, convert units to match (e.g., converting km/h to m/s).

Calculating Speed, Distance, and Time Examples Table
Problem Type	Description	Steps to Solve	Example
Calculating Distance	Finding the distance traveled based on speed and time.	Identify the speed \( S \) (in km/h or m/s). Identify the time \( t \) (in hours or seconds). Use the formula for distance: \( \text{Distance} = \text{Speed} \times \text{Time} \).	If \( S = 60 \, \text{km/h} \) and \( t = 2 \, \text{hours} \), the distance is \( \text{Distance} = 60 \times 2 = 120 \, \text{km} \).
Calculating Speed	Finding the speed of an object when distance and time are known.	Identify the distance \( D \) (in km or meters). Identify the time \( t \) (in hours or seconds). Use the formula for speed: \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \).	If \( D = 120 \, \text{km} \) and \( t = 2 \, \text{hours} \), the speed is \( \text{Speed} = \frac{120}{2} = 60 \, \text{km/h} \).
Calculating Time	Finding the time taken to travel a certain distance at a given speed.	Identify the distance \( D \) (in km or meters). Identify the speed \( S \) (in km/h or m/s). Use the formula for time: \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \).	If \( D = 120 \, \text{km} \) and \( S = 60 \, \text{km/h} \), the time is \( \text{Time} = \frac{120}{60} = 2 \, \text{hours} \).
Calculating Speed on Different Terrains	Finding the speed of an object on different terrains (if friction or other factors affect speed).	Identify the distance \( D \) and time \( t \) (as usual). Consider how the terrain (e.g., road type, roughness) affects the speed. Use the formula \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \), adjusting the speed if necessary based on terrain factors.	If the distance is \( D = 100 \, \text{km} \), but the terrain slows the speed to \( 40 \, \text{km/h} \), you would calculate the time as \( \text{Time} = \frac{100}{40} = 2.5 \, \text{hours} \).