Speed and Velocity

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. On this page, change the time to see how a car's speed links to the area under the v-t graph.

What is Speed?

🚗 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

Time (s)5s

Reading the Speed-Time Graph

📊 Hidden Meanings

①Horizontal line in a v-t graph = constant motion

②Area under the graph = distance

③Slope = acceleration (0 for constant speed)

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?

Speed = distance traveled ÷ time taken.

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?

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.

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

Speed = distance ÷ time (① wrong), and velocity is a vector with both magnitude and direction (③ wrong).

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).

← Previous

Hydrosphere & Seawater

Inertia

Was this helpful? Support seegongsik