Last reviewed: 7 November 2026
Updated November 2026. These Grade 9 speed, velocity and acceleration notes cover speed in km/h and m/s, converting between them, average speed, the difference between speed and velocity, and acceleration. Speed = distance ÷ time. To change km/h to m/s, multiply by 1,000 and divide by 3,600 (or simply divide by 3.6): 72 km/h = 20 m/s. Acceleration is the change in velocity divided by the time taken.
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 9 maths topics, see our Grade 9 maths revision guide and the Grade 9 notes hub. Longitudes and local time, the other part of this sub-strand, are covered in our latitude, longitude and time notes.
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What the Grade 9 Curriculum Covers
“Time, Distance and Speed” is a sub-strand under Measurements in the Kenya Institute of Curriculum Development’s Grade 9 Mathematics design. Learners work out speed in km/h and m/s, average speed, velocity and acceleration, and relate longitudes to local time. The design is listed on the KICD Grade Nine curriculum designs page. This page covers the speed, velocity and acceleration parts.
Speed in km/h and m/s
Speed = distance ÷ time, so distance = speed × time and time = distance ÷ speed. Keep units matching: kilometres with hours, metres with seconds.
Converting units
- km/h to m/s: divide by 3.6. 90 km/h = 90 ÷ 3.6 = 25 m/s.
- m/s to km/h: multiply by 3.6. 15 m/s = 15 × 3.6 = 54 km/h.
Why 3.6? 1 km/h = 1,000 m ÷ 3,600 s = 1/3.6 m/s.
Worked example: a race
A runner covers 400 m in 80 seconds. Speed = 400 ÷ 80 = 5 m/s. In km/h: 5 × 3.6 = 18 km/h.
Average Speed
Average speed = total distance ÷ total time. It is not the average of the speeds, unless equal times are spent at each speed.
Worked example
In this made-up trip, a matatu travels 120 km in 2 hours, then 60 km in 1 hour 30 minutes.
- Total distance: 120 + 60 = 180 km.
- Total time: 2 + 1.5 = 3.5 h.
- Average speed: 180 ÷ 3.5 ≈ 51.4 km/h.
Averaging the two speeds (60 and 40 km/h) gives 50 km/h, which is wrong because the matatu spent different times at each speed. Also convert minutes to hours as decimals: 30 min = 0.5 h, not 0.3 h.
Speed and Velocity
Speed tells you how fast something moves. Velocity tells you how fast and in which direction, as explained in OpenStax College Physics’ section on time, velocity and speed. Two cars moving at 60 km/h, one going north and one going south, have the same speed but different velocities. A runner who completes one full lap of a track ends where she started, so her average velocity for the lap is zero even though her average speed is not.
Acceleration
Acceleration is the rate of change of velocity: acceleration = (final velocity − initial velocity) ÷ time. In m/s per second, the unit is m/s². This matches OpenStax College Physics’ section on acceleration.
Worked example: speeding up
A car starts from rest and reaches 20 m/s in 8 seconds. Acceleration = (20 − 0) ÷ 8 = 2.5 m/s².
Worked example: slowing down
A bus moving at 15 m/s brakes to 3 m/s in 4 seconds. Acceleration = (3 − 15) ÷ 4 = −3 m/s². The negative sign shows it is slowing down; this is often called deceleration (or retardation) of 3 m/s².
Worked example: mixed units
A boda boda speeds up from 18 km/h to 54 km/h in 5 seconds. Convert first: 18 km/h = 5 m/s and 54 km/h = 15 m/s. Acceleration = (15 − 5) ÷ 5 = 2 m/s².
Original Practice Questions With Worked Answers
- Convert 108 km/h to m/s. 108 ÷ 3.6 = 30 m/s.
- How long does a train at 80 km/h take to travel 200 km? 200 ÷ 80 = 2.5 h = 2 hours 30 minutes.
- A cyclist rides 30 km in 1.5 h and 10 km in 0.5 h. Find the average speed. 40 ÷ 2 = 20 km/h.
- A ball’s velocity changes from 2 m/s to 14 m/s in 3 s. Find the acceleration. 12 ÷ 3 = 4 m/s².
- What is the difference between speed and velocity? Velocity includes direction; speed does not.
Cover the answers and attempt each question first. For timed practice, use the Grade 9 revision papers or the Grade 9 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
How do you convert km/h to m/s?
Divide by 3.6. For example, 36 km/h = 10 m/s. To go back, multiply by 3.6.
How do you calculate average speed?
Divide the total distance by the total time taken, including any stops.
What is the formula for acceleration?
Acceleration = (final velocity − initial velocity) ÷ time taken, usually in m/s².
What does negative acceleration mean?
The object is slowing down in the direction of motion. This is often called deceleration.