Compound Measures flashcards
10 cards on Compound Measures: the key points, worked examples and the slips to watch. Swipe through them, or print them.
Card 1 of 10
Compound Measures
Speed, distance and time
How do you use speed = distance ÷ time, and rearrange it for distance or time?
Answer it in your head, then turn the card over.
Speed, distance and time
Key points
- Speed is the distance covered in each unit of time.
- The units go together: km and hours give km/h; metres and seconds give m/s.
Formulae
speed = distance ÷ time
distance = speed × time
time = distance ÷ speed
135 miles at 54 mph
Time = 135 ÷ 54 = 2.5 hours
0.5 hours is half an hour, 30 minutes: 2 hours 30 minutes
Watch out
Rearranging the wrong way, as time = speed × distance: 135 × 54 hours cannot be right.
Compound Measures
Minutes as parts of an hour
How do you change minutes into hours for a speed calculation, and change hours back?
Answer it in your head, then turn the card over.
Minutes as parts of an hour
Key points
- Divide the minutes by 60: an hour has 60 minutes, not 100.
- Fractions are often neater: 20 minutes is hour, 45 minutes is hour.
- Hours back to minutes: multiply the decimal part by 60.
Cycling at 36 km/h for 40 minutes
40 minutes = = hour
Distance = 36 × = 24 km
And 2.25 hours is 2 hours and 0.25 × 60 = 15 minutes
Watch out
20 minutes is not 0.2 hours: it is 20 ÷ 60 = hour, and 0.2 hours is only 12 minutes.
Compound Measures
Density, mass and volume
How do you use density = mass ÷ volume, and rearrange it for mass or volume?
Answer it in your head, then turn the card over.
Density, mass and volume
Key points
- Density is how much mass is packed into each unit of volume.
- The units follow what you put in: grams and cm³ give g/cm³.
- The same mass of a denser material takes up less space.
Formulae
density = mass ÷ volume
mass = density × volume
volume = mass ÷ density
Example
3860 g of gold at 19.3 g/cm³: volume = 3860 ÷ 19.3 = 200 cm³
15 cm³ of a metal at 7.8 g/cm³: mass = 7.8 × 15 = 117 g
Watch out
A mass in kg with a volume in cm³ gives kg/cm³: convert one first to get the units asked for.
Compound Measures
Pressure, force and area
How do you use pressure = force ÷ area, and why does a smaller area give a bigger pressure?
Answer it in your head, then turn the card over.
Pressure, force and area
Key points
- Pressure is a force spread over an area.
- Newtons on square metres give N/m², also called pascals (Pa).
- The same force on a smaller area gives a bigger pressure: that is why a drawing pin goes in point first.
Formulae
pressure = force ÷ area
force = pressure × area
area = force ÷ pressure
Example
A 450 N box on 0.3 m²: pressure = 450 ÷ 0.3 = 1500 N/m²
2000 N/m² over 0.25 m²: force = 2000 × 0.25 = 500 N
Watch out
Dividing by an area under 1 m² makes the answer bigger: 450 ÷ 0.3 is 1500, not 135.
Compound Measures
Converting m/s and km/h
How do you convert a speed between m/s and km/h?
Answer it in your head, then turn the card over.
Converting m/s and km/h
Key points
- Change one unit at a time.
- m/s to km/h: × 3600 gives metres in an hour, then ÷ 1000 gives km. That is × 3.6 in all.
- km/h to m/s: ÷ 3.6.
- Sense check: the km/h number is always bigger than the m/s number.
Example
25 m/s: 25 × 3600 = 90 000 m in an hour, which is 90 km/h
108 km/h: 108 ÷ 3.6 = 30 m/s
Watch out
Multiplying by 60 or by 1000 on its own changes only one of the two units.
Compound Measures
Converting g/cm³ and kg/m³
How do you convert a density from g/cm³ to kg/m³?
Answer it in your head, then turn the card over.
Converting g/cm³ and kg/m³
Key points
- 1 m³ = 100 cm × 100 cm × 100 cm = 1 000 000 cm³.
- So × 1 000 000 gives the grams in a cubic metre, then ÷ 1000 gives kilograms.
- Overall, g/cm³ to kg/m³ is × 1000.
2.7 g/cm³ in kg/m³
2.7 × 1 000 000 = 2 700 000 g in a cubic metre
÷ 1000 = 2700 kg, so 2700 kg/m³
Watch out
1 m³ is not 100 cm³: each of its three lengths is 100 cm, so it holds 1 000 000 cm³.
Compound Measures
Distance–time graphs
What does a distance–time graph show, and how do you read an average speed from it?
Answer it in your head, then turn the card over.
Distance–time graphs
Key points
- The gradient of the line is the speed: steeper means faster.
- A flat section means stopped: the distance is not changing.
- Average speed = total distance ÷ total time, with any stops included in the time.
A run in three parts
10 km in 1 hour, a 30-minute stop, then 5 km in 30 minutes
Total distance: 10 + 5 = 15 km
Total time: 1 + 0.5 + 0.5 = 2 hours
Average speed = 15 ÷ 2 = 7.5 km/h
Watch out
Leaving out the stop: its 30 minutes still count in the total time.
Compound Measures
Average speed over a journey in parts
Why can't you find the average speed of a journey by averaging the speeds of its parts?
Answer it in your head, then turn the card over.
Average speed over a journey in parts
Key points
- Average speed is total distance ÷ total time.
- A slower part takes longer, so it fills more of the time.
- Find each part's time first, with time = distance ÷ speed.
40 km at 20 km/h, then 40 km at 40 km/h
Times: 40 ÷ 20 = 2 hours, and 40 ÷ 40 = 1 hour
Average speed = 80 ÷ 3 = 26.7 km/h (1 d.p.)
Watch out
Averaging 20 and 40 gives 30 km/h, which is too fast: the slow part took twice as long.
Compound Measures
HigherVelocity–time graphs: acceleration
What does the gradient of a velocity–time graph show?
Answer it in your head, then turn the card over.
Velocity–time graphs: acceleration
Key points
- The gradient is the acceleration: the change in velocity ÷ the time taken.
- A downward slope is a deceleration, a negative acceleration.
- A flat section is a steady speed, not stopped: stopped is a flat line along 0.
Formula
acceleration = change in velocity ÷ time taken
Example
0 to 15 m/s in 6 s: 15 ÷ 6 = 2.5 m/s²
20 m/s down to 8 m/s in 4 s: (8 − 20) ÷ 4 = −3 m/s²
Watch out
A flat line here is not a stop: that reading belongs to a distance–time graph.
Compound Measures
HigherVelocity–time graphs: distance
How do you find the distance travelled from a velocity–time graph?
Answer it in your head, then turn the card over.
Velocity–time graphs: distance
Key points
- The distance travelled is the area under the graph.
- Split the area into triangles, rectangles or trapezia, then add them up.
- Triangle: ½ × base × height. Trapezium: ½(a + b)h.
0 to 15 m/s in 6 s, then steady for 10 s
Triangle: ½ × 6 × 15 = 45 m
Rectangle: 10 × 15 = 150 m
Distance = 45 + 150 = 195 m
Watch out
Forgetting the ½ for a triangle doubles that part of the distance.
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Put it into practice
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