On a displacement-time graph, what does the gradient of the graph tell you?

The gradient of a displacement-time graph is the velocity of the object. A positive gradient means the object is moving forwards , and a negative gradient means it is moving backwards . The steeper the line, the greater the speed.

True or False? A horizontal section of a displacement-time graph shows that the object is moving at a constant velocity.

False. A horizontal section of a displacement-time graph means the displacement is not changing, so the object is stationary . Strictly, a stationary object does have a constant velocity , of zero, so the word doing the work in the statement is moving . A constant non-zero velocity gives a straight sloping line on a displacement-time graph, not a horizontal one; it is on a velocity -time graph that a horizontal line means constant velocity.

On a displacement-time graph, what does a straight section tell you, and what does a curved section tell you?

On a displacement-time graph, a straight section shows the object moving at a constant velocity , because the gradient, and so the velocity, is the same all the way along it. A curved section shows the velocity changing , so the object is accelerating or decelerating . The gradient of a curve is different at every point.

What does it mean if a displacement-time graph touches the time axis?

Where a displacement-time graph touches the time axis the displacement is zero , so the object is at the fixed origin that its displacement is measured from. This does not mean the object has stopped. An object is stationary only where the graph is horizontal .

On a displacement-time graph, what does the value where the graph meets the vertical axis represent?

Where a displacement-time graph meets the vertical axis, the value is the object's initial displacement : how far it is from the fixed origin at time zero. An object does not have to start at the origin, so this value is not always zero. A graph starting at 100 m, for example, could show someone setting out on a walk from a point 100 m from their house.

On a velocity-time graph, what does the gradient of the graph tell you?

The gradient of a velocity-time graph is the acceleration of the object. A straight line means the acceleration is constant , and a horizontal line means the acceleration is zero, so the object is moving at a constant velocity .

On a velocity-time graph, what does the area between the graph and the time axis represent?

The area between a velocity-time graph and the time axis gives the change in displacement of the object over that time. Where the graph is above the axis the object is moving forwards, so that area is travel in the positive direction. Where the graph is below the axis the object is moving backwards.

What does it mean if a velocity-time graph touches the time axis?

Where a velocity-time graph touches the time axis the velocity is zero , so the object is instantaneously at rest . If the graph crosses the axis rather than only touching it, the velocity changes sign, so the object changes direction at that moment.

True or False? A section of a velocity-time graph that lies below the time axis always shows an object that is slowing down.

False. Below the time axis on a velocity-time graph the velocity is negative, so the object is moving backwards . Whether it is speeding up or slowing down is decided by the gradient , not by which side of the axis it is on. Below the axis, a negative gradient means the object is speeding up as it moves backwards, and a positive gradient means it is slowing down while still moving backwards.

Why can a velocity-time graph go below the time axis when a speed-time graph cannot?

Velocity is a vector , so it can be negative, and a negative velocity is drawn below the time axis to show motion in the backward direction. Speed is a scalar : it is the size of the velocity and can never be negative, so a speed-time graph never goes below the axis. On a speed-time graph, motion backwards still appears as a positive speed, with the graph coming down to touch the axis at the moment the direction changes.

Define an acceleration-time graph .

An acceleration-time graph shows the acceleration of an object moving in a straight line, on the vertical axis, against time on the horizontal axis. It can lie above the time axis, on it, or below it.

On an acceleration-time graph, what does the area between the graph and the time axis represent?

It represents the change in velocity over that interval. It is neither the velocity itself nor a displacement: the graph records only how fast the velocity is changing, so an area can only tell you how much the velocity has changed.

A car's acceleration-time graph is a horizontal line, which then drops to the time axis and stays there. What is the car doing in each of the two stages?

In the first stage the acceleration is constant , so the car's velocity changes at a steady rate. In the second stage the acceleration is zero , so the velocity stops changing and the car carries on at whatever constant velocity it had reached. Zero acceleration does not mean the car has stopped.

True or False? An acceleration-time graph that lies entirely above the time axis shows an object whose velocity is positive throughout.

False. A graph above the axis shows the velocity increasing , which says nothing about what the velocity actually is. An object that set off with a large negative velocity is still travelling backwards while its velocity climbs, so you cannot tell the sign of the velocity without knowing its initial value.

An object is moving backwards , and its acceleration-time graph lies below the time axis. Is it speeding up or slowing down?

It is speeding up . Below the axis the acceleration is negative, so the velocity is decreasing, and for an object already moving backwards a decreasing velocity means it is going faster and faster in the backward direction. A decreasing velocity and a decreasing speed are not the same thing.

Why does an acceleration-time graph for a multi-stage journey have vertical jumps in it?

Because the object switches from one constant acceleration to another instantaneously , for instance from braking at a steady rate to travelling at a constant velocity. The acceleration takes one value up to that moment and a different value after it, with no time in between for it to pass through the values between, so the graph is drawn as a set of separate horizontal segments.

A journey is described as decelerating for 20 s, holding a constant speed for 8 s, then decelerating to rest. How many straight sections will its velocity-time graph have, and what happens where they join?

It will have three straight sections. At each join the velocity is the same on both sides, so the sections meet end to end and the graph is unbroken. What changes at a join is the gradient , not the height, so a velocity-time graph never jumps the way an acceleration-time graph does.

International A Level (IAL)MathsEdexcelMechanics 1FlashcardsKinematics (Straight Line Motion)Kinematics Graphs

Kinematics Graphs (Edexcel International A Level (IAL) Maths: Mechanics 1): Flashcards

Exam code: YMA01

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FrontDisplacement-Time Graphs
On a displacement-time graph, what does the gradient of the graph tell you?
BackDisplacement-Time Graphs
False.
A horizontal section of a displacement-time graph means the displacement is not changing, so the object is stationary.
Strictly, a stationary object does have a constant velocity, of zero, so the word doing the work in the statement is moving.
A constant non-zero velocity gives a straight sloping line on a displacement-time graph, not a horizontal one; it is on a velocity-time graph that a horizontal line means constant velocity.

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Cards in this collection (26)

On a displacement-time graph, what does the gradient of the graph tell you?
The gradient of a displacement-time graph is the velocity of the object.
A positive gradient means the object is moving forwards, and a negative gradient means it is moving backwards.
The steeper the line, the greater the speed.
True or False?
A horizontal section of a displacement-time graph shows that the object is moving at a constant velocity.
False.
A horizontal section of a displacement-time graph means the displacement is not changing, so the object is stationary.
Strictly, a stationary object does have a constant velocity, of zero, so the word doing the work in the statement is moving.
A constant non-zero velocity gives a straight sloping line on a displacement-time graph, not a horizontal one; it is on a velocity-time graph that a horizontal line means constant velocity.
On a displacement-time graph, what does a straight section tell you, and what does a curved section tell you?
On a displacement-time graph, a straight section shows the object moving at a constant velocity, because the gradient, and so the velocity, is the same all the way along it.
A curved section shows the velocity changing, so the object is accelerating or decelerating. The gradient of a curve is different at every point.
What does it mean if a displacement-time graph touches the time axis?
Where a displacement-time graph touches the time axis the displacement is zero, so the object is at the fixed origin that its displacement is measured from.
This does not mean the object has stopped. An object is stationary only where the graph is horizontal.
Fill in the blanks to complete the two formulas for a journey:
$average speed = \frac{total______travelled}{time taken}$
$average velocity = \frac{______from the starting point}{time taken}$
The completed formulas for a journey are:
$average speed = \frac{total distance travelled}{time taken}$
$average velocity = \frac{displacement from the starting point}{time taken}$
Average speed uses distance, so it can never be negative. Average velocity uses displacement, so it can be positive, negative or zero: an object that finishes where it started has an average velocity of zero, however far it has travelled.
How do you find the total distance travelled from a displacement-time graph?
To find the total distance travelled from a displacement-time graph, add together the size of every rise and every fall, ignoring whether it goes up or down.
So, for example, a graph that rises by 11 m and then falls by 11 m back to where it started shows a total distance travelled of $11 + 11 = 22$ m, even though the displacement at the end is zero.
On a displacement-time graph, what does the value where the graph meets the vertical axis represent?
Where a displacement-time graph meets the vertical axis, the value is the object's initial displacement: how far it is from the fixed origin at time zero.
An object does not have to start at the origin, so this value is not always zero. A graph starting at 100 m, for example, could show someone setting out on a walk from a point 100 m from their house.
On a velocity-time graph, what does the gradient of the graph tell you?
The gradient of a velocity-time graph is the acceleration of the object.
A straight line means the acceleration is constant, and a horizontal line means the acceleration is zero, so the object is moving at a constant velocity.
On a velocity-time graph, what does the area between the graph and the time axis represent?
The area between a velocity-time graph and the time axis gives the change in displacement of the object over that time.
Where the graph is above the axis the object is moving forwards, so that area is travel in the positive direction. Where the graph is below the axis the object is moving backwards.
A velocity-time graph goes both above and below the time axis. Fill in the blanks:
total displacement $=$ (sum of the areas above the axis) $______$ (sum of the areas below the axis)
total distance travelled $=$ (sum of the areas above the axis) $______$ (sum of the areas below the axis)
The completed rules for a velocity-time graph are:
total displacement $=$ (sum of the areas above the axis) $-$ (sum of the areas below the axis)
total distance travelled $=$ (sum of the areas above the axis) $+$ (sum of the areas below the axis)
An area below the axis is travel backwards. It brings the object back towards its starting point, so it reduces the displacement, but it still adds to how far the object has actually moved.
What does it mean if a velocity-time graph touches the time axis?
Where a velocity-time graph touches the time axis the velocity is zero, so the object is instantaneously at rest.
If the graph crosses the axis rather than only touching it, the velocity changes sign, so the object changes direction at that moment.
True or False?
A section of a velocity-time graph that lies below the time axis always shows an object that is slowing down.
False.
Below the time axis on a velocity-time graph the velocity is negative, so the object is moving backwards. Whether it is speeding up or slowing down is decided by the gradient, not by which side of the axis it is on.
Below the axis, a negative gradient means the object is speeding up as it moves backwards, and a positive gradient means it is slowing down while still moving backwards.
How do you calculate the area between a velocity-time graph and the time axis when the graph is made up of straight sections?
To find the area under a velocity-time graph made of straight sections, split the region into triangles, rectangles and trapezia, work out each area separately, and add them.
So, for example, a section falling at a constant rate from $40 {m s}^{- 1}$ to $12 {m s}^{- 1}$ over 20 seconds encloses a trapezium of area $\frac{1}{2} (40 + 12) (20) = 520$ m.
Why can a velocity-time graph go below the time axis when a speed-time graph cannot?
Velocity is a vector, so it can be negative, and a negative velocity is drawn below the time axis to show motion in the backward direction.
Speed is a scalar: it is the size of the velocity and can never be negative, so a speed-time graph never goes below the axis.
On a speed-time graph, motion backwards still appears as a positive speed, with the graph coming down to touch the axis at the moment the direction changes.
Define an acceleration-time graph.
An acceleration-time graph shows the acceleration of an object moving in a straight line, on the vertical axis, against time on the horizontal axis.
It can lie above the time axis, on it, or below it.
On an acceleration-time graph, what does the area between the graph and the time axis represent?
It represents the change in velocity over that interval.
It is neither the velocity itself nor a displacement: the graph records only how fast the velocity is changing, so an area can only tell you how much the velocity has changed.
Fill in the blanks to complete what each side of the time axis means on an acceleration-time graph:
A region above the axis is an $______$ in velocity, and a region below the axis is a $______$ in velocity.
The completed statement is:
A region above the axis is an increase in velocity, and a region below the axis is a decrease in velocity.
So the total change in velocity since the start is the sum of the areas above the axis minus the sum of the areas below it.
A car's acceleration-time graph is a horizontal line, which then drops to the time axis and stays there. What is the car doing in each of the two stages?
In the first stage the acceleration is constant, so the car's velocity changes at a steady rate.
In the second stage the acceleration is zero, so the velocity stops changing and the car carries on at whatever constant velocity it had reached.
Zero acceleration does not mean the car has stopped.
True or False?
An acceleration-time graph that lies entirely above the time axis shows an object whose velocity is positive throughout.
False.
A graph above the axis shows the velocity increasing, which says nothing about what the velocity actually is.
An object that set off with a large negative velocity is still travelling backwards while its velocity climbs, so you cannot tell the sign of the velocity without knowing its initial value.
An object is moving backwards, and its acceleration-time graph lies below the time axis. Is it speeding up or slowing down?
It is speeding up.
Below the axis the acceleration is negative, so the velocity is decreasing, and for an object already moving backwards a decreasing velocity means it is going faster and faster in the backward direction.
A decreasing velocity and a decreasing speed are not the same thing.
A velocity-time graph has velocity in ${m s}^{- 1}$ on the vertical axis and time in seconds on the horizontal axis. Fill in the blanks with the units of each:
the gradient of the graph: $______$
the area between the graph and the time axis: $______$
The completed units are:
the gradient of the graph: ${m s}^{- 2}$
the area between the graph and the time axis: $m$
A gradient divides the vertical unit by the horizontal one and an area multiplies them, which is why labelling both axes with their units is worth the trouble.
A train decelerates uniformly from $40 {m s}^{- 1}$ to $12 {m s}^{- 1}$ in 20 seconds. Find its deceleration.
Uniformly means at a constant rate, so divide the change in velocity by the time taken:
$\frac{12 - 40}{20} = - 1.4 {m s}^{- 2}$
The acceleration is $- 1.4 {m s}^{- 2}$ , so the deceleration is $1.4 {m s}^{- 2}$ : a deceleration is quoted as a positive number, because the word itself carries the sign.
Why does an acceleration-time graph for a multi-stage journey have vertical jumps in it?
Because the object switches from one constant acceleration to another instantaneously, for instance from braking at a steady rate to travelling at a constant velocity.
The acceleration takes one value up to that moment and a different value after it, with no time in between for it to pass through the values between, so the graph is drawn as a set of separate horizontal segments.
A journey is described as decelerating for 20 s, holding a constant speed for 8 s, then decelerating to rest. How many straight sections will its velocity-time graph have, and what happens where they join?
It will have three straight sections.
At each join the velocity is the same on both sides, so the sections meet end to end and the graph is unbroken.
What changes at a join is the gradient, not the height, so a velocity-time graph never jumps the way an acceleration-time graph does.
True or False?
A displacement-time graph can be drawn below the time axis.
True.
Displacement is a vector, so it can be negative, and a negative displacement puts the object on the opposite side of its starting point.
A graph running down to $- 5$ m shows an object that has passed back through its starting point and gone 5 m beyond it.
A journey's velocity-time graph splits into areas of 520, 96 and $6 (T - 28)$ , and the total displacement is 730 m. How do you find $T$ ?
Add the three areas and set the total equal to the known displacement, which turns the unknown into an ordinary equation:
$520 + 96 + 6 (T - 28) = 730$
That gives $6 (T - 28) = 114$ , so $T - 28 = 19$ and $T = 47 s$ .

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