Real-Life Graphs Flashcards

All 21 cards in this deck

What does the gradient of a distance-time graph represent?

The speed.
Steeper line = faster speed.

What does a horizontal line on a distance-time graph tell you?

The object is stationary (not moving).
The distance from the start stays the same.

What are the steps to find the speed for one stage of a distance-time graph?

e.g. a cyclist travels 20 km in the first 15 minutes

1. Read the distance travelled in that stage: $20$ km
2. Read the time taken, in the units you want: $15$ min $= \frac{15}{60}$ h
3. Speed $=$ distance $\div$ time $= 20 \div \frac{15}{60} = 80$ km/h

True or false? On a distance-time graph, a line sloping downwards means the object is slowing down.

False.
It means the object is travelling back towards its starting point.

On a distance-time graph, how do you identify the section where the speed is greatest?

The section whose gradient is greatest (the steepest section).

How do you draw a missing section of a travel graph when you are told the speed and the time?

e.g. 75 km/h for the last 20 minutes

Work out the distance for that section, then draw a straight line rising by that distance over that time.
$75 \times \frac{20}{60} = 25$ km, so the line rises 25 km over the 20 minutes.

What does the gradient of a speed-time graph represent?

The acceleration.

What does a horizontal line on a speed-time graph tell you?

The speed is constant (acceleration is zero).

True or false? A horizontal line on a speed-time graph means the object is stationary.

False.
It means constant speed; the object is only stationary if that speed is 0.

On a speed-time graph with speed in m/s and time in seconds, what are the units of the gradient?

m/s$^2$ (metres per second per second).

What is a conversion graph?

A straight line graph used to convert between two quantities or units, e.g. pounds and euros.

What are the steps to use a conversion graph?

e.g. convert 20 miles to kilometres

1. Find 20 on the miles axis
2. Go vertically up to the line
3. Read horizontally across to the km axis: about 32 km

True or false? A conversion graph can be used to convert in both directions.

True.
Start on either axis, go to the line, then read off the other axis.

True or false? Every conversion graph passes through the origin.

False.
E.g. a °C to °F graph crosses at 32 °F when the temperature is 0 °C.

What does the gradient of a conversion graph represent?

e.g. euros (y-axis) against pounds (x-axis)

The conversion rate — how many of the y-unit there are per 1 of the x-unit.
Here: the number of euros per £1.

How can you use a conversion graph for a value larger than the graph goes up to?

e.g. convert 200 miles when the graph stops at 50 miles

Convert a value that fits, then scale up.
Read 50 miles $\approx$ 80 km, then $\times 4$ gives about 320 km.

What does the gradient of a real-life straight line graph represent?

The rate of change of the y-quantity with respect to the x-quantity.
e.g. on a cost against units of electricity graph, the cost of each unit.

What are the steps to interpret the gradient of a real-life straight line graph?

e.g. cost in £ (y-axis) against units of electricity used (x-axis)

1. Gradient $=$ change in $y \div$ change in $x$
2. Give its units: £ per unit of electricity
3. Say it in context: the cost of each unit of electricity

What does the intercept on the vertical axis of a real-life graph represent?

e.g. a graph of volume $L$ litres against time $t$ seconds crosses at $L = 4$

The value of the y-quantity when $x = 0$ — the starting value.
Here: there were 4 litres in the container at the start.

True or false? On a graph of volume of petrol in a tank against distance travelled, a negative gradient means the car is slowing down.

False.
It means petrol is being used up as distance increases; the gradient is litres used per km.

What shape is the graph of time taken against speed for a fixed journey distance?

A reciprocal curve ($t = \frac{d}{s}$).
As speed increases the time falls, getting close to the axes but never touching them.