Speed and Distance-Time Graphs
AdvancedSpeed = distance ÷ time. On a distance-time graph the slope is the speed: steeper is faster, a horizontal line means stationary; average speed = total distance ÷ total time.
- Speed = distance ÷ time; distance = speed × time; time = distance ÷ speed.
- Common units are m/s and km/h — convert before comparing.
- On a distance-time graph the slope is the speed: steeper is faster.
文體小知識：科普知識文章用生活實例解釋科學概念，先看現象再講原理，讀完就能解釋日常見到的東西。
§Text Passage
1Fast and slow sound subjective, but physics turns them into numbers: speed. Speed = distance ÷ time — 60 km in one hour is 60 km/h; 6 m in two seconds is 3 m/s.
2With the formula, knowing any two quantities gives the third: distance = speed × time (3 m/s for 10 s is 30 m), time = distance ÷ speed (120 km at 60 km/h is 2 hours). Always match the units before comparing speeds.
3A distance-time graph draws the whole journey as one line: time across, distance up. The steeper the line, the greater the speed; a flat stretch means the distance is unchanged — the object is resting. Rise, flat, then a steeper rise: travel, stop, speed up.
4Long journeys speed up and slow down, so we summarise with average speed = total distance ÷ total time. Having learned to describe motion, the next lesson asks something deeper: why do you lurch forward when a bus brakes suddenly?
1Summary 重點摘要
Speed = distance ÷ time. On a distance-time graph the slope is the speed: steeper is faster, a horizontal line means stationary; average speed = total distance ÷ total time.
2Vocabulary cards Vocabulary
The distance travelled per unit of time — distance divided by time.
The unit of speed, symbol m/s: 1 m/s means 1 metre each second, about 3.6 km/h.
The everyday unit of speed, symbol km/h, shown on car speedometers.
A graph with time on the horizontal axis and distance on the vertical axis; the slope of the line gives the speed.
How steep a line is: on a distance-time graph steeper means faster, and a horizontal line means stationary.
Motion at constant speed; its distance-time graph is a straight sloping line.
The total distance divided by the total time taken.
The gauge that shows a vehicle's current speed.
3Step by step Steps
- The speed formulaSpeed describes how fast an object moves, with the formula speed = distance ÷ time: Mary walks 40 m in 20 s, so her speed is 40 ÷ 20 = 2 m/s. Knowing any two of the three quantities, substitute into the formula to find the third — the foundation of all motion calculations. Race officials and navigation systems rely on this simple relation, showing the power of a basic formula.
- Knowing the unitsSpeed units must be converted before comparison: walking is about 1.5 m/s, cycling about 5 m/s, a town car about 50 km/h — the two units cannot be compared directly. Remember 1 m/s = 3.6 km/h: 50 km/h is roughly 14 m/s, clearly far faster than a bicycle. Road signs use km/h while science uses m/s, so conversion is a fundamental skill in problem solving.
- Finding distanceRearranging gives distance = speed × time: running at 3 m/s for 10 s covers 3 × 10 = 30 m. The formula suits estimating journeys: walking to school at about 1.5 m/s for 10 minutes — 600 s — covers roughly 900 m, which fixes a sensible departure time. Logistics firms planning deliveries and runners planning training distances depend on this same simple relation.
- Finding timeRearrange again for time = distance ÷ speed: driving 120 km at 60 km/h takes 120 ÷ 60 = 2 hours. Budgeting a journey before setting off makes scheduling more accurate — to know whether you can catch a film on time, work out the drive first and add a margin. Long trip planning and freight scheduling both rest on this calculation; the difference between late and on time often lies in this one step.
- Reading graphs: slopeOn a distance-time graph the slope stands for speed: in one chart, if line A is steeper than line B, A moves faster — the steeper the line, the quicker the motion. A horizontal stretch means the distance is unchanged, so the object is stationary, for example at a rest stop. Compare slopes only within the same graph and the same units; lines on two different charts cannot be compared by eye. Reading the slope is reading the heart of the graph.
- Reading a whole journeyRead a complete journey section by section: a graph that rises steeply, goes flat, then rises even more steeply shows steady travel, a rest stop, then faster travel. Work out the speed of each section from its slope before forming an overall picture; for average speed divide total distance by total time, rest time included. Reading in sections is the basic method for handling complex journey data and deserves practice.
4Diagrams Diagrams
5Worked example Example
Example: a bus travels at 60 km/h for 1.5 h, rests at a stop for 0.5 h, then drives 1 h at 80 km/h. Find the average speed and describe the distance-time graph.
- First leg distance = 60 × 1.5 = 90 km.
- During the rest the distance stays at 90 km — a horizontal section on the graph.
- Third leg distance = 80 × 1 = 80 km, so total = 90 + 80 = 170 km; total time = 1.5 + 0.5 + 1 = 3 h.
- Average speed = 170 ÷ 3 ≈ 56.7 km/h.
- Answer: First leg: 90 km; rest: distance unchanged; third leg: 80 km. Total 170 km in 3 hours, average speed = 170 ÷ 3 ≈ 56.7 km/h. The rest time must be counted, or the result comes out too large; the graph rises, flattens, then rises more steeply.
6Common mistakes Mistakes
7Quick check Quick check
Q1Write the formula for speed.
Q2Mary walks at 2 m/s for 30 s. How far does she go?
Q3What does a horizontal line on a distance-time graph mean?
Q4A car covers 160 km at 80 km/h. How long does it take?
Q5A journey of 100 km takes 2 hours. What is the average speed?
8Recap Recap
- Speed = distance ÷ time; distance = speed × time; time = distance ÷ speed.
- Common units are m/s and km/h — convert before comparing.
- On a distance-time graph the slope is the speed: steeper is faster.
- A horizontal line means stationary.
- Average speed = total distance ÷ total time.