Calculating journeys from linear speed-time graphs | Maths

Starter quiz

Speed = __________

speed $\times$ time

time $\times$ distance

speed $\div$ time

distance $\div$ time ✓

time $\div$ distance
Speed is the rate at which something is moving. It is measured as the distance travelled per unit of __________.

speed

time ✓

miles

hours

mph
Which of these graphs shows a constant speed?
The area of the shaded shape is ______ square units.

'18' ✓
The area of the shaded shape is ______ square units.

'30' ✓
The area of the shaded shape is ______ square units.

'28' ✓

Exit quiz

On a speed-time graph the __________ bound by the graph and horizontal axis tells us the distance travelled.

length

distance

area ✓

speed

volume
Which calculation would find how far is travelled between $0$ and $4$ seconds?

$4\times12=48$ metres

$6\times18=108$ metres

${1\over2}\times4\times12=24$ metres ✓

${1\over2}\times6\times18=54$ metres

$12$ metres
Calculate how far the particle travelled between $4$ and $6$ seconds.

'30 metres' ✓
How far has the particle modelled in this graph travelled after $6$ seconds? ______ metres.

'90' ✓
How far has the particle modelled in this graph travelled between $0$ and $3$ seconds?

Half the whole area under the graph up to $6$ seconds.

${{1\over2}(10+16)\times{3}}$ metres

$(2\times14)+\left({{1\over2}(14+16)\times{1}}\right)$ metres ✓

$(2\times14)+\left({{1\over2}(14+16)\times{3}}\right)$ metres

$(3\times14)+\left(\frac{1}{2}\right)$ metres
How far has the particle modelled in this graph travelled after $6$ seconds? ______ metres.

'100' ✓

Worksheet

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Lesson Details

Key learning points

Distance travelled is calculated by multiplying speed and time.
This is represented on a speed-time graph by the area bound by the graph and the x axis.
Calculating this area gives the total distance travelled.

Common misconception

Calculating area by counting squares rather than looking at the scales.

Remind pupils that often on speed-time graphs the scales on the axes will be different. Check the scales before calculating distance. Check the final answer is realistic in context.

Keywords

Compound shape - A compound shape is a shape created using two or more basic shapes.