Speed is the distance travelled divided by the time taken, and it tells you only how fast something is going.
Velocity is that speed with a direction attached, so 100 km/h is a speed and 100 km/h due north is a velocity.
On a speed-time graph the area under the line is the distance travelled, and a flat horizontal line means the speed is not changing: uniform motion.
The car in the picture below moves at 30 m per second, so as you change the time, the distance it has covered and the shaded area on the graph grow together.
What is speed?
If you write down only how fast something moves and leave out the direction, you cannot tell apart two motions at the same pace in opposite directions. That is why we keep two quantities: speed, which measures size only, and velocity, which includes direction. Speed is the distance travelled divided by the time taken; velocity is that size with a direction attached, a vector. A car's speedometer reads speed, with no direction, while a weather forecast saying "north-westerly wind at 5 m per second" is giving a velocity.
🚗 Farther in the same time means faster
①Of two things moving for the same time, the one that goes farther is faster
②Of two things covering the same distance, the one that takes less time is faster
③To compare both cases with one number, we find the distance covered in a fixed time such as one second or one hour; that is speed
④speed = distance travelled ÷ time taken
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A car driving at 30 m per second past marks on a road, with the distance covered and the speed shown as time passes
The road in the top picture has marks every 50 m from 0 m to 300 m, and the car drives from left to right at 30 m per second. Each extra second moves the car a little less than one mark (50 m), and at 10 seconds it reaches the 300 m mark. The blue arrow is the distance from the start to the car; the time and distance are written at the top left, and the speed, distance divided by time, at the top right. The speed stays at 30 m/s whatever the time, because this car is in uniform motion.
5 s
Reading a speed-time graph
Speed and velocity are easy to treat as one word, but a round trip pulls them apart. Walk to a shop 1 km from home and back in 20 minutes, and you have covered 2 km, an average speed of 6 km/h. Yet you ended where you started, so the change in position (displacement) is zero, and the average velocity, displacement divided by time, is zero too. An average velocity of zero does not mean you stood still; keeping that in mind keeps the two ideas apart.
📊 The area is the distance
①On a speed-time graph a flat horizontal line means uniform motion at a constant speed
②The area under the line is speed × time, so it equals the distance travelled
③The line on this graph is at 30 m/s, so the rectangle shaded up to 5 s has an area of 30 × 5 = 150 m
④In the picture above, at the same 5 s, the car is at the 150 m mark
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Speed-time graph for motion at a constant 30 m/s, with the area shaded up to the chosen time equal to the distance travelled
Speed and velocity
🧭 With or without direction
①Speed has size only (a scalar) and tells you how fast
②Velocity has both size and direction (a vector) and tells you how fast and which way
③100 km/h is a speed; 100 km/h due north is a velocity
④Something going round a circle at a steady speed keeps changing direction, so its velocity keeps changing
Summary
Formula for speed
v = dt
Units: m/s or km/h
Converting units
1 m/s = 3.6 km/h
An hour is 3600 s and a kilometre is 1000 m, so multiplying m/s by 3.6 gives km/h
🎯 Points that often come up
①speed = distance travelled ÷ time taken, in m/s or km/h
②On a speed-time graph the area under the line is the distance travelled
③Speed is a scalar with size only; velocity is a vector with size and direction
④Uniform motion appears on a speed-time graph as a flat horizontal line
⑤To change km/h to m/s divide by 3.6; to change m/s to km/h multiply by 3.6
Worked examples and unit test
Example 1
A car travelling at a constant speed takes 20 s to cover 100 m. What is its speed in m/s?
1
Speed is found by dividing the distance travelled by the time taken.
2
100 m ÷ 20 s = 5 m/s.
▸ 5 m/s
It covers 5 m every second. The car in the picture above (30 m/s) is six times as fast.
Example 2
How many m/s is 72 km/h? Is this value a speed or a velocity, and what must be added to make it a velocity?
1
1 m/s = 3.6 km/h, so to turn km/h into m/s you divide by 3.6. 72 ÷ 3.6 = 20, so it is 20 m/s.
2
A value with size only, like 72 km/h, is a speed; add a direction, such as "20 m/s due north", and it becomes a velocity.
▸ 20 m/s; with no direction it is a speed, and adding a direction makes it a velocity
A motorway limit of 100 km/h is about 28 m/s, roughly 28 m every second.
Unit Test
Which statement about speed and velocity is correct?
①Speed = time taken ÷ distance traveled
②On a speed-time graph, the area under the graph represents the distance traveled
③Velocity has only magnitude and no direction
④1 m/s is faster than 3.6 km/h
⑤Uniform motion is a slanted line on a speed-time graph
▸ ② On a speed-time graph, the area under the graph represents the distance traveled
1
Speed = distance ÷ time (① wrong), and velocity is a vector with both magnitude and direction (③ wrong).
2
1 m/s = 3.6 km/h, the same speed (④ wrong), and uniform motion is a horizontal line on a v-t graph (⑤ wrong); the area under a v-t graph is the distance traveled (② correct).