Speed and Velocity

Calculate speed from distance and time, and learn why velocity also needs a direction.

About 3 min read
  • Calculate speed, distance and time
  • Explain the difference between speed and velocity
  • Calculate average speed for a journey
Before you start

You can rearrange simple equations and convert minutes into seconds. Both skills help in speed calculations.

Speed

Speed tells us how much distance an object covers in a certain time. A runner who covers 100 m in 10 s has a speed of 10 m/s. Most journeys are not perfectly steady, so we usually calculate an average speed for the whole trip.

Speed equation

speed = distance ÷ time

Definition: average speed

Total distance travelled divided by total time taken.

Velocity

Speed has only a size. Velocity has both a size and a direction. Two cars moving at 20 m/s in opposite directions have the same speed but different velocities. If an object changes direction, its velocity changes even when its speed stays the same.

Definition: velocity

Speed in a stated direction.

Average speed

A cyclist travels 3 km in 10 minutes. Find the average speed in m/s.

Maths
distance = 3 km = 3000 m
time = 10 min = 600 s
speed = 3000 ÷ 600 = 5 m/s

Answer: 5 m/s

Match your units

Convert distance and time before you calculate if the question asks for m/s.

Exam focus
Say it like this“Velocity is 12 m/s north.”
Not like this“Velocity is 12 m/s.” — A velocity needs a direction as well as a size.
Common mistakeAveraging two speeds instead of dividing total distance by total time.

Practice

A sprinter runs 200 m in 25 s. Find the speed.
200 ÷ 25 = 8 m/s.
A bus travels at 15 m/s for 40 s. How far does it go?
distance = speed × time = 15 × 40 = 600 m.
How long does it take to walk 120 m at 1.5 m/s?
time = distance ÷ speed = 120 ÷ 1.5 = 80 s.
Going further
A car travels 60 km in 1 hour, then 30 km in 1 hour. Find its average speed.
Total distance is 90 km and total time is 2 hours, so average speed = 45 km/h.

Quick check

Speed and velocity quick check

Which equation gives distance?

Rearranging speed = distance ÷ time by multiplying both sides by time gives this result.

Which is a velocity?

It includes a size and a direction, which is what velocity requires.

A car goes around a roundabout at steady speed. What changes?

Its direction keeps changing, so this directional quantity changes too.
Key takeaways
  • Speed = distance ÷ time.
  • Average speed uses total distance and total time.
  • Velocity is speed in a stated direction.
  • Check the units before calculating.
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