Speed and Velocity

Calculating speed from distance and time, and seeing how velocity adds direction.

  • Define and explain Speed and Velocity in your own words
  • Use key terms such as speed accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

Describing motion precisely is the first step to predicting it. With a few equations and some clever graphs, you can work out how fast anything moves — from a sprinter to a satellite. This chapter turns journeys into numbers.

This lesson focuses on Speed and Velocity: calculating speed from distance and time, and seeing how velocity adds direction.

Definition: Speed and Velocity

Calculating speed from distance and time, and seeing how velocity adds direction.

Key ideas

Speed tells you how fast, velocity tells you how fast and where to

Speed = distance ÷ time is a scalar with no direction. Velocity adds direction, making it a vector. Two cars can share a speed of 20 m/s yet have different velocities if they head opposite ways — and that difference matters in collisions.

Graphs turn journeys into pictures

On a distance–time graph, the gradient (slope) equals the speed — steeper means faster, flat means stationary. On a velocity–time graph the gradient gives acceleration, and the area under the line gives the distance travelled. One graph can replace a whole table of data.

Key term — speed: How fast something moves: distance travelled divided by time taken, measured in m/s or km/h.

Worked example: Speed and Velocity

How is distance found from a velocity–time graph?

It equals the area under the graph, between the line and the time axis.

Answer: It equals the area under the graph, between the line and the time axis.

Common mistakes
  • Reading the gradient of a velocity–time graph as speed The gradient of a velocity–time graph is acceleration; speed is read straight off the vertical axis.
  • Mixing up distance and displacement Distance is the total path travelled; displacement is the straight line from start to end — they match only on a straight one-way trip.

Practice

A train rounds a bend at a constant 40 m/s. Is it accelerating? Explain.
Velocity includes direction.

Yes — its direction is changing, so its velocity is changing, which means it is accelerating even though its speed is constant.

On a distance–time graph, what does a flat horizontal section mean?
Is the distance changing?

The object is stationary — distance is not changing as time passes.

A runner covers 100 m in 12.5 s. Calculate the average speed.
Divide distance by time.

100 ÷ 12.5 = 8 m/s.

A car travels at a steady 25 m/s for 40 s. How far does it go?
Rearrange: distance = speed × time.

25 × 40 = 1000 m.

Quick check

Speed and Velocity — quick check

Which of these best defines "speed"?

How fast something moves: distance travelled divided by time taken, measured in m/s or km/h.

A van accelerates from 10 m/s to 22 m/s in 6 s. Find the acceleration.

(22 − 10) ÷ 6 = 12 ÷ 6 = 2 m/s².
Key takeaways
  • Speed and Velocity: calculating speed from distance and time, and seeing how velocity adds direction.
  • Speed tells you how fast, velocity tells you how fast and where to: Speed = distance ÷ time is a scalar with no direction.
  • velocity: Speed in a stated direction — a vector, so 30 m/s north and 30 m/s south are different velocities.
  • Watch out for: reading the gradient of a velocity–time graph as speed