What does a distance-time graph show?

A distance-time graph shows how the distance of an object from a point changes over time .

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

A horizontal line on a distance-time graph represents an object that is not moving (it is stationary ).

True or False? If a distance-time grap h has a positive gradient then the object is moving further away from the original point.

True. If a distance-time grap h has a positive gradient then the object is moving further away from the original point.

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

The gradient of a distance-time graph represents the speed at which the object is moving.

True or False? If a distance-time grap h has a straight line then the speed of the object is increasing .

False. If a distance-time grap h has a straight line then the speed of the object is constant .

What does a speed-time graph show?

A speed-time graph shows how the speed of an object changes over time .

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

A horizontal line on a speed-time graph represents an object moving with a constant speed .

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

The gradient of a speed-time graph represents the acceleration of the object.

What does the area underneath a speed-time graph represent?

The area underneath a speed-time graph represents the distance that the object has travelled.

True or False? If a speed-time grap h has a negative gradient then the object is slowing down .

True. If a speed-time grap h has a negative gradient then the object is slowing down .

True or False? When a speed-time graph touches the horizontal axis , it means that the object is back where it started .

False. When a speed-time graph touches the horizontal axis , it means that the object is not moving (it is at rest ).

True or False? A rate-of-change graph must always have time on the horizontal axis.

False. Time is the commonest choice, but any two variables can be plotted against each other. The volume of air in an inflating balloon plotted against its radius is a rate-of-change graph with no time on it at all.

What does the gradient of a tangent to a curved graph estimate?

It estimates the rate of change at that particular point , since the rate is no longer constant along a curve. Where the curve is steeper the rate of change is greater, and the tangent's gradient is only an estimate because the tangent is drawn by eye.

Water flows at a constant rate into a container that gets narrower towards the top. What does its depth-time graph look like?

Its gradient starts shallow and becomes steeper , because the same volume of water each second fills a narrower space and so raises the depth more quickly. A container with vertical sides would instead give a straight line, since the depth would rise at a constant rate throughout.

A straight-line graph is used to model fuel remaining against distance travelled. Why might that model not be realistic?

A straight line assumes fuel is used at a constant rate for the whole journey. In practice the rate changes with speed, traffic and load, so a more realistic graph would be a curve.

IGCSEMathsEdexcelMaths BFlashcardsFunctionsReal-Life Graphs

Real-Life Graphs (Edexcel IGCSE Maths B): Flashcards

Exam code: 4MB1

1/18

0Still learning

Know0

FrontDistance-Time Graphs
What does a distance-time graph show?

Was this flashcard helpful?

Cards in this collection (18)

What does a distance-time graph show?
A distance-time graph shows how the distance of an object from a point changes over time.
What does a horizontal line on a distance-time graph represent?
A horizontal line on a distance-time graph represents an object that is not moving (it is stationary).
True or False?
If a distance-time graph has a positive gradient then the object is moving further away from the original point.
True.
If a distance-time graph has a positive gradient then the object is moving further away from the original point.
What does the gradient of a distance-time graph represent?
The gradient of a distance-time graph represents the speed at which the object is moving.
True or False?
If a distance-time graph has a straight line then the speed of the object is increasing.
False.
If a distance-time graph has a straight line then the speed of the object is constant.
What does a speed-time graph show?
A speed-time graph shows how the speed of an object changes over time.
What does a horizontal line on a speed-time graph represent?
A horizontal line on a speed-time graph represents an object moving with a constant speed.
What does the gradient of a speed-time graph represent?
The gradient of a speed-time graph represents the acceleration of the object.
What does the area underneath a speed-time graph represent?
The area underneath a speed-time graph represents the distance that the object has travelled.
True or False?
If a speed-time graph has a negative gradient then the object is slowing down.
True.
If a speed-time graph has a negative gradient then the object is slowing down.
True or False?
When a speed-time graph touches the horizontal axis, it means that the object is back where it started.
False.
When a speed-time graph touches the horizontal axis, it means that the object is not moving (it is at rest).
Define the rate of change of $y$ against $x$ .
It is the amount that $y$ changes for every 1 unit of increase in $x$ , and on a graph it is measured by the gradient.
A straight line means that rate is constant, and a horizontal line means it is zero, so $y$ is not changing at all.
How do you work out the units of a gradient?
Divide the units on the $y$ -axis by the units on the $x$ -axis.
A graph of volume in cubic centimetres against time in seconds therefore has a gradient measured in cubic centimetres per second.
True or False?
A rate-of-change graph must always have time on the horizontal axis.
False.
Time is the commonest choice, but any two variables can be plotted against each other.
The volume of air in an inflating balloon plotted against its radius is a rate-of-change graph with no time on it at all.
A graph of fuel in litres against distance in kilometres has gradient $- 0.09$ . What does that mean?
The units are litres per kilometre, so travelling 1 km uses up 0.09 litres of fuel.
The gradient is negative because the amount of fuel left in the tank is decreasing as the distance increases.
What does the gradient of a tangent to a curved graph estimate?
It estimates the rate of change at that particular point, since the rate is no longer constant along a curve.
Where the curve is steeper the rate of change is greater, and the tangent's gradient is only an estimate because the tangent is drawn by eye.
Water flows at a constant rate into a container that gets narrower towards the top. What does its depth-time graph look like?
Its gradient starts shallow and becomes steeper, because the same volume of water each second fills a narrower space and so raises the depth more quickly.
A container with vertical sides would instead give a straight line, since the depth would rise at a constant rate throughout.
A straight-line graph is used to model fuel remaining against distance travelled. Why might that model not be realistic?
A straight line assumes fuel is used at a constant rate for the whole journey.
In practice the rate changes with speed, traffic and load, so a more realistic graph would be a curve.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Previous:Estimating GradientsNext:Differentiation

More Revision Notes you might like