Real-Life Graphs Flashcards

All 23 cards in this deck

What does a horizontal line on a distance-time graph mean?

The object is stationary (not moving).
The distance stays the same as time passes.

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

The speed.
The steeper the line, the faster the speed.

On a distance-time graph, what does a straight line sloping back down to the time axis show?

Travelling back towards the starting point, reaching it when the line meets the axis.

True or false? A horizontal line on a distance-time graph means the object is moving at a steady speed.

False.
It means the object is stationary; a sloping straight line means a steady speed.

What are the steps to work out a speed from one section of a distance-time graph?
e.g. a section showing 20 km travelled in 15 minutes

1. Read the distance travelled: $20$ km
2. Read the time taken, in hours: $15$ min $= 0.25$ h
3. Speed $=$ distance $\div$ time $= 20 \div 0.25 = 80$ km/h

What are the steps to complete a travel graph for a described journey?
e.g. at 3 hours she is 5 km from home, stays 2 hours, then walks home in 1 hour 30 minutes

1. Draw a horizontal line for the stop: $(3, 5)$ to $(5, 5)$
2. Find the end point: home is $0$ km at $5 + 1.5 = 6.5$ hours
3. Join with a straight line: $(5, 5)$ to $(6.5, 0)$

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

The acceleration.

What does a horizontal line on a speed-time graph show?

Constant (steady) speed — no acceleration.

What does a line sloping downwards on a speed-time graph show?

The object is slowing down (decelerating).

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

False.
It means constant speed; the object is only stopped where the line is on the time axis (speed $= 0$).

On a speed-time graph, how can you tell which of two sections has the greater acceleration?

The steeper section has the greater acceleration.

How do you find the speed at a given time from a speed-time graph?
e.g. the speed at 10 seconds

Read up from $10$ on the time axis to the line, then straight across to the speed axis.

What is a conversion graph?

A straight line graph used to change between two units or currencies by reading from one axis to the other.

What are the steps to convert a value using a conversion graph?
e.g. convert 120 kg to stones

1. Find $120$ on the kilograms axis
2. Go straight up to the line
3. Go across to the stones axis and read off: $19$ stones

How do you convert a value that is larger than the largest value shown on a conversion graph?
e.g. 80 ounces when the graph only goes up to 20 ounces

Read off a factor of it and scale up, or read off two values that add to it and add the readings.
e.g. read $20$ ounces in grams, then multiply by $4$.

True or false? To convert in the opposite direction you need a different conversion graph.

False.
The same line works both ways — start from the other axis and read across.

How do you draw a conversion graph when you are told one pair of equivalent values?
e.g. 5 miles = 8 km

Plot $(0, 0)$ and $(5, 8)$, then join them with a straight line and extend it across the grid.

When a conversion graph question says "You must show how you get your answer", what must you show?

The readings taken from the graph (lines drawn on it) and the scaling up or adding you did with them.

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

The rate of change of the $y$ quantity per unit of the $x$ quantity.
e.g. litres per second.

A graph shows the volume of water, $V$ litres, in a tank at time $t$ seconds. What does the gradient represent?

The rate of change of volume — how fast the water is flowing in or out, in litres per second.

On a graph of pay (£) against hours worked, what does the gradient tell you?

The hourly rate of pay — how much is paid for each hour worked.

On a line graph of temperature against time, how do you find the time at which a given temperature occurred?
e.g. when the liquid was at 50 °C

Read across from $50$ on the temperature axis to the line, then straight down to the time axis.

True or false? On a line graph over time, a steeper section means the quantity is changing more quickly.

True.
A steeper gradient means a faster rate of change.