The Solar Car Battery

Year 9 · Linear Relationships

# The Solar Car Battery

Modelling and comparing two electric cars

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## The two cars

Tested under average city driving — **40 km** covered each hour.

<div class="cards">
<div class="card zet-card fragment"><h3 class="zet">Zet</h3>Starts at 80 kWh Drains 20 kWh per hour</div>
<div class="card spark-card fragment"><h3 class="spark">Spark</h3>Starts at 60 kWh Drains 12 kWh per hour</div>
</div>

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## A rule for each battery

Battery power *P* (kWh) after *t* hours:

intercept = starting charge (where the line begins)

gradient = the drop each hour — negative, because power falls (−20, −12)

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## After 3 hours

The Spark is already ahead — even though it began with less charge.

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## Solve for a target power

When is 40 kWh left?

Get the t-term alone, then divide — answers can be fractions.

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## Which lasts longer?

Flat when *P* = 0:

Spark wins 👈 slower drain beats bigger start.

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## When are they equal?

Set the two rules equal:

👈

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## How far on one charge?

Distance = 40 km/h × (time until flat)

<div class="cols">
<div class="fragment"><div class="big zet">160</div>km · Zet · flat at 4 h</div>
<div class="fragment"><div class="big spark">200</div>km · Spark · flat at 5 h</div>
</div>

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## A rule from two points — the Watt

Two readings: (1, 60) and (4, 20)

m = gradient · c = intercept (the starting charge)

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## How far does the Watt go?

Empty when *P* = 0:

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## Putting it on a graph

Two straight lines, crossing at **(2.5, 30)**.

plot the start on the P-axis, step down by the gradient, join with a ruler; label axes & both lines; mark where they cross.