Speed is distance traveled divided by time, and it only tells how fast something moves.
Velocity is a vector that adds direction to speed, so 100 km/h is speed while 100 km/h north is velocity.
On a speed-time graph the area under the curve is the distance traveled, and a horizontal line means constant speed.
Change the time and how a car's speed links to the area under the v-t graph appears.
What is Speed?
If you write only how fast something goes and drop the direction, two motions that are equally fast in opposite ways get lumped together as the same. Directionless size obtained by dividing the path length by the time taken is speed; that size with a direction attached is the velocity vector. On a speed–time graph the area under the line equals the path length, and a flat horizontal line means the speed stays constant. Reading a sentence without a direction as speed, and one with a direction as velocity, keeps leftover fastness after a round trip from being mixed with displacement.
🚗 Intuition — How Fast a Car Moves
①In the same time, a car going farther is faster
②"How fast" expressed as a number is speed
③Speed = distance ÷ time
seegongsik.com
A car moving along a road; speed is computed from distance and time
Road marks sit every 50 m from 0 m to 300 m, and the car is placed on a forward mark in proportion to the chosen time from 0 s through 10 s. Time, distance, and speed in m/s are written at the top; when time is greater than 0, a blue line from the start mark to the car shows the distance. The speed–time graph drawn for the same time has a speed axis from 0 to 40 and a green horizontal line fixed at 30 m/s. Up to the current instant the region under that line is filled, the phrase area = distance sits in the middle, and a dashed line and a point mark that instant. Changing the time updates the car’s place and the width of the filled rectangle together.
5s
Reading the Speed-Time Graph
Speed and velocity are easy to use as if they were one word, but speed is a scalar with size only and velocity is a vector that carries a direction. Going out and returning to the same place can leave a long path while displacement is near 0, and then average velocity can be small. Average speed divides the path length by time; average velocity divides displacement by time. If you do not first ask whether a graph or a sentence has a direction, a round trip whose displacement is 0 gets written as if the speed were 0 too.
📊 Hidden Meanings
①Horizontal line in a v-t graph = constant motion
②Area under the graph = distance
③Slope = acceleration (0 for constant speed)
④This sketch uses 30 m/s
seegongsik.com
Speed-time graph showing distance as the area under the curve
Speed vs Velocity
🧭 The Difference
①Speed: scalar (magnitude only) — how fast
②Velocity: vector (magnitude + direction) — how fast in which direction
③100 km/h is speed; 100 km/h north is velocity
Summary
Speed Formula
v = dt
Units: m/s or km/h
Unit Conversion
1 m/s = 3.6 km/h
Multiply by 3.6
🎯 Exam Points
①Speed = distance ÷ time, unit m/s
②v-t graph area = distance
③Speed is scalar, velocity is vector
④Constant motion: horizontal v-t graph
⑤km/h → m/s: divide by 3.6
Examples and Unit Test
Example 1
A car travels 100 m in 20 seconds at a constant speed. What is the speed of the car in m/s?
1
Speed = distance traveled ÷ time taken.
2
Speed = 100 m ÷ 20 s = 5 m/s.
▸ 5 m/s (100 ÷ 20 = 5)
The farther something goes in the same time, the greater its speed.
Example 2
How many m/s is a speed of 72 km/h? Is this value a speed or a velocity, and what must be added to make it a velocity?
1
Since 1 m/s = 3.6 km/h, you convert km/h to m/s by dividing by 3.6: 72 ÷ 3.6 = 20 m/s.
2
A value like 72 km/h with only magnitude is a speed (scalar); adding a direction, as in "20 m/s to the north", makes it a velocity (vector).
▸ 20 m/s (72 ÷ 3.6) / with no direction it is speed, adding a direction makes it velocity
Speed gives only magnitude, while velocity gives magnitude and direction together.
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).