A scalar is a quantity that has only a size (magnitude) and no direction. Distance, speed, mass and time are all scalar quantities.

A vector is a quantity that has both a size (magnitude) and a direction . Displacement, velocity, acceleration and force are all vector quantities.

True or False? A speed can be negative if an object is moving backwards.

False. Speed is a scalar , so it has a size but no direction, and it cannot be negative. It is the velocity that is negative when an object moves in the direction chosen as negative. Its speed is the size of that velocity.

Define fundamental units .

Fundamental units , also called S.I. units , are the internationally agreed standard units of measurement. The three needed in mechanics are the metre (m) for length, the second (s) for time and the kilogram (kg) for mass. Every other unit in mechanics is built from these.

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Quantities, Units & Modelling (Cambridge (CIE) A Level Maths: Mechanics): Flashcards

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Define scalar.

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Cards in this collection (18)

Define scalar.
A scalar is a quantity that has only a size (magnitude) and no direction.
Distance, speed, mass and time are all scalar quantities.
Two cars are travelling along a straight road, with one having a velocity of $7 {m s}^{- 1}$ and the other having a velocity of $- 7 {m s}^{- 1}$ . What does the difference in sign tell you about their motion?
The two cars are travelling at the same speed but in opposite directions.
Velocity is a vector, so the sign records the direction of travel. Which direction counts as positive is a choice made at the start of a problem.
Define vector.
A vector is a quantity that has both a size (magnitude) and a direction.
Displacement, velocity, acceleration and force are all vector quantities.
True or False?
A speed can be negative if an object is moving backwards.
False.
Speed is a scalar, so it has a size but no direction, and it cannot be negative.
It is the velocity that is negative when an object moves in the direction chosen as negative. Its speed is the size of that velocity.
Complete the definitions of these two vector quantities:
Displacement is the $______$ moved in a given direction from a starting point.
Velocity is the $______$ of an object in a given direction.
Displacement is the distance moved in a given direction from a starting point.
Velocity is the speed of an object in a given direction.
How are vector quantities written in printed material such as textbooks and exam papers, and how should you write them by hand?
In print a vector is written in bold, upright type, for example $F$ .
Bold cannot be reproduced in handwriting, so by hand a vector is underlined instead.
Define fundamental units.
Fundamental units, also called S.I. units, are the internationally agreed standard units of measurement.
The three needed in mechanics are the metre (m) for length, the second (s) for time and the kilogram (kg) for mass.
Every other unit in mechanics is built from these.
Complete the conversions between units of length and of mass:
$1 km =______m$
$1 m =______cm$
$1 kg =______g$
The completed conversions are:
$1 km = 1000 m$
$1 m = 100 cm$
$1 kg = 1000 g$
Lengths must be converted into metres and masses into kilograms before they are used in a calculation.
A time is given as 17 minutes and 42 seconds. Convert it into S.I. units.
The time is 1062 seconds.
Each minute is 60 seconds, so $17 \times 60 = 1020$ seconds, and $1020 + 42 = 1062$ seconds.
True or False?
To convert a time given in hours into seconds, you multiply by 60.
False.
Multiplying by 60 converts hours into minutes. Hours are converted into seconds by multiplying by 60 twice, which is multiplying by 3600.
For example, $3.8$ hours is $3.8 \times 3600 = 13680$ seconds.
Convert $0.054$ grams into kilograms, giving your answer in standard form.
The mass is $5.4 \times 10^{- 5} kg$ .
There are 1000 grams in a kilogram, so grams are divided by 1000: $0.054 \div 1000 = 0.000054$ .
Define derived unit.
A derived unit is a unit built by combining the fundamental units of length, time and mass.
For example, a velocity is a distance divided by a time, so it is measured in ${m s}^{- 1}$ .
Convert a speed of $5.8 {km h}^{- 1}$ into ${m s}^{- 1}$ , giving your answer to 3 significant figures.
The speed is $1.61 {m s}^{- 1}$ .
There are 1000 metres in a kilometre and 3600 seconds in an hour, so $5.8 \times 1000 \div 3600 = 1.611 \dots$
Fill in the missing S.I. units:
Velocity is measured in $______$ , acceleration is measured in $______$ , and force is measured in $______$ .
Velocity is measured in ${m s}^{- 1}$ , acceleration is measured in ${m s}^{- 2}$ , and force is measured in newtons (N), which is the same as ${kg m s}^{- 2}$ .
When converting an acceleration from ${km h}^{- 2}$ into ${m s}^{- 2}$ , why do you divide by $3600^{2}$ rather than by $3600$ ?
The unit of time is squared in ${km h}^{- 2}$ , so the conversion factor for time has to be squared as well.
One hour is 3600 seconds, so $1 {km h}^{- 2} = 1000 \div 3600^{2} {m s}^{- 2}$ .
True or False?
Speed and velocity are measured in the same units.
True.
Speed and velocity are both measured in ${m s}^{- 1}$ .
A velocity is a speed together with a direction, and adding a direction does not change the unit.
For a density is given as $14 {g cm}^{- 3}$ , converting it into ${kg m}^{- 3}$ means dividing by 1000 for the mass, but multiplying by $100^{3}$ for the volume. Why multiply?
In ${g cm}^{- 3}$ the centimetres are in the denominator, so that part of the conversion works the opposite way round.
One metre is 100 cm, so one cubic metre holds $100^{3}$ cubic centimetres, and a quantity given per cubic centimetre is $100^{3}$ times as much per cubic metre.
Here $14 \div 1000 \times 100^{3} = 14000 {kg m}^{- 3}$ .
Speed is measured in ${m s}^{- 1}$ . What does that unit tell you about the formula for speed?
The unit ${m s}^{- 1}$ means metres divided by seconds, which is a distance divided by a time, so
$speed = \frac{distance}{time}$
A forgotten formula can often be rebuilt this way, from the units the quantity is measured in.

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