By Thread Academy · 19 September 2026 · Physics
Speed, velocity and acceleration are among the most commonly mixed-up ideas in physics. They describe how motion happens, but each one measures something different. Once you can keep them apart and use their equations confidently, a large part of mechanics starts to feel straightforward.
Speed: how fast something moves
Speed is the distance travelled per unit of time. It tells you how fast something is moving, but says nothing about direction.
The equation is:
speed = distance / time
In symbols, this is often written as v = s / t. The standard units are metres per second (m/s).
Worked example 1: Calculating speed
Question: A runner completes 400 m in 52 s. Calculate their average speed.
Step 1: Write down what you know. Distance s = 400 m, time t = 52 s.
Step 2: Use the equation speed = distance / time.
Step 3: Substitute: 400 / 52 = 7.69 (to 3 significant figures).
Answer: The runner's average speed is 7.69 m/s.
Speed vs velocity: scalars and vectors
Velocity is speed in a given direction. It is the same as speed, except that direction matters.
This is the difference between a scalar and a vector:
- Scalar quantities have size only. Speed, distance and time are scalars.
- Vector quantities have size and direction. Velocity, displacement and acceleration are vectors.
Direction matters because of round trips. Imagine you cycle 6 km to the shops and 6 km back home in one hour. Your average speed is 12 km/h. But your average velocity is 0 km/h, because you ended up back where you started — your overall displacement is zero.
Unit conversions
Exam questions often give distance in kilometres and time in hours, or ask for an answer in m/s. The conversion to remember is:
1 m/s = 3.6 km/h
To convert km/h to m/s, divide by 3.6. To convert m/s to km/h, multiply by 3.6.
Worked example 2: Unit conversion
Question: A car travels at 72 km/h. Express this speed in m/s.
Step 1: Recall that to go from km/h to m/s, divide by 3.6.
Step 2: Calculate 72 / 3.6 = 20.
Answer: The car travels at 20 m/s.
Acceleration: the rate of change of velocity
Acceleration is how quickly velocity changes. If a car speeds up, slows down or changes direction, it is accelerating. Slowing down is sometimes called deceleration, but physicists just treat it as acceleration in the opposite direction.
The equation is:
a = (v - u) / t
Here u is the initial velocity, v is the final velocity, and t is the time taken. The units are metres per second squared (m/s^2).
Worked example 3: Calculating acceleration
Question: A train accelerates from 10 m/s to 34 m/s in 8 s. Calculate its acceleration.
Step 1: Write down what you know. u = 10 m/s, v = 34 m/s, t = 8 s.
Step 2: Use a = (v - u) / t.
Step 3: Substitute: (34 - 10) / 8 = 24 / 8 = 3.
Answer: The acceleration is 3 m/s^2.
Worked example 4: Rearranging for time
Question: A cyclist slows from 12 m/s to rest with an acceleration of -3 m/s^2. How long does it take to stop?
Step 1: Rearrange a = (v - u) / t to make t the subject: t = (v - u) / a.
Step 2: Note that "to rest" means v = 0 m/s. Substitute: (0 - 12) / (-3) = -12 / -3 = 4.
Answer: It takes 4 s to stop.
Distance-time graphs: reading motion at a glance
A distance-time graph plots distance on the vertical axis against time on the horizontal axis. You can read the motion directly from its shape:
- A straight line going upward means constant speed. A steeper line means a higher speed.
- A horizontal line means the object is stationary — distance is not changing.
- A curved line means the speed is changing: a curve getting steeper means speeding up, a curve flattening means slowing down.
The gradient (slope) of the line equals the speed. If the distance axis is in metres and time in seconds, a gradient of 5 gives a speed of 5 m/s.
A common mistake to avoid
Many students use distance where they should use displacement, and confuse speed with velocity on questions involving direction. If a question mentions a return journey or asks about direction, switch from scalars to vectors. If it only asks "how fast", speed is enough.
Key takeaways
- Speed is distance per unit time (v = s/t); velocity is speed in a given direction.
- Scalars have size only; vectors have size and direction.
- Convert km/h to m/s by dividing by 3.6; convert m/s to km/h by multiplying by 3.6.
- Acceleration is the rate of change of velocity: a = (v - u) / t, measured in m/s^2.
- On a distance-time graph, the gradient of the line equals the speed.