Distance-Time Graphs

Question 1

What does a distance-time graph show?

Answer 1

A distance-time graph shows how the distance travelled by an object changes over time.

Question 2

When can distance travelled be represented on a distance-time graph?

Answer 2

If an object moves along a straight line, the distance it travels can be represented (or plotted) on a distance-time graph.

Question 3

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

Answer 3

The gradient (steepness) of a distance-time graph tells you the speed of the object.

Question 4

How does the steepness of a distance-time graph relate to speed?

Answer 4

The greater the gradient, and therefore the steeper the line, the faster the object is moving.

Question 5

How is gradient defined on a graph?

Answer 5

On a graph, the gradient is defined as the change in the ‘y’ value divided by the change in the ‘x’ value. It defines how steep a line is.

On a distance-time graph, this means gradient = change in distance (vertical axis) divided by change in time (horizontal axis).

Question 6

Why does gradient equal speed on a distance-time graph?

Answer 6

Speed is calculated as distance divided by time. On a distance-time graph, distance is shown on the vertical axis and time on the horizontal axis. Therefore, speed = change in vertical axis ÷ change in horizontal axis, which is the gradient.

Question 7

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

Answer 7

A flat horizontal line means the object is stationary. This means it is stopped and its distance is not changing over time.

Question 8

What does a straight line that is not horizontal show on a distance-time graph?

Answer 8

A straight line that is not horizontal indicates that the object is travelling at a constant speed. Straight uphill sections mean it is travelling at a steady speed.

Question 9

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

Answer 9

A curved line represents that the object is accelerating or decelerating. This means its speed is changing.

Question 10

What does accelerating mean?

Answer 10

Accelerating means the speed of an object is increasing. Acceleration is the rate of change in speed (or velocity) and is measured in metres per second squared (m/s²).

Question 11

What does decelerating mean?

Answer 11

A → Decelerating means slowing down or negative acceleration. For example, a car slowing down is undergoing deceleration.

Question 12

How is acceleration or deceleration shown on a distance-time graph?

Answer 12

A → Acceleration or deceleration is shown as a curved line on a distance-time graph, because the speed (and therefore the gradient) is changing.

Question 13

What does a curve that is getting steeper on a distance-time graph mean?

Answer 13

A → A curve that is getting steeper means the gradient is increasing. This means the speed is increasing, so the object is accelerating. This is described as a steepening curve or curving upwards.

Question 14

What does a curve that is getting less steep on a distance-time graph mean?

Answer 14

A curve that is getting less steep means the gradient is decreasing. This means the speed is decreasing, so the object is decelerating. This is described as a levelling off curve or curving downwards, getting shallower or flatter.

Question 15

How can you describe Section 1 of a typical distance-time graph example with a straight line?

Answer 15

Section 1 shows a straight line, which means the object is travelling at a constant speed.

Question 16

How can you describe Section 2 of a typical distance-time graph example with a flat line?

Answer 16

Section 2 shows a flat horizontal line, which means the object is stationary.

Question 17

How can you describe Section 3 of a typical distance-time graph example with a steepening curve?

Answer 17

Section 3 shows a curved line that is getting steeper. This means the gradient is increasing, the speed is increasing, and therefore the object is accelerating.

Question 18

How can you describe Section 4 of a typical distance-time graph example with a curve getting less steep?

Answer 18

Section 4 shows a curved line that is getting less steep. This means the gradient is decreasing, the speed is decreasing, and therefore the object is decelerating.

Question 19

How can you describe Section 5 of a typical distance-time graph example with a straight downward line?

Answer 19

Section 5 shows a straight line, meaning the object is travelling at a constant speed. The fact that the line goes downwards tells you the object is travelling back to a distance of 0, meaning it is travelling backwards to return to its starting position.

Question 20

How can you find the speed of an object at a particular time if the graph is curved?

Answer 20

If the graph is curved (meaning the object is accelerating or decelerating), you can find its speed at a particular time by drawing a tangent to the curve at that point and finding the gradient of the tangent.

Question 21

What is a tangent in the context of a distance-time graph?

Answer 21

A tangent is a straight line that just touches a point on a curve. It is drawn at a specific point to find the gradient at that exact time.

Question 22

How do you calculate speed from a tangent on a distance-time graph?

Answer 22

After drawing the tangent, work out the change in distance (vertical change) and the change in time (horizontal change). Since gradient = vertical change ÷ horizontal change, this gives the speed at that particular time.

Question 23

Can an object be accelerating even if its speed is constant? 🟠

Answer 23

Yes. An object moving at a constant speed but continually changing direction is also accelerating because velocity changes if either the magnitude (speed) or the direction changes.

Question 24

Why is direction important when considering acceleration? 🟠

Answer 24

Velocity is a vector quantity, meaning it has both magnitude and direction. If either the magnitude or the direction changes, velocity changes. This is important when dealing with circular motion, where direction is constantly changing even if speed stays the same.