Velocity-Time Graphs

Question 1

Q1 → What is a velocity–time graph and what does it show?
A velocity–time graph shows how an object’s velocity changes as it travels over time. If an object moves along a straight line, its motion can be represented using this type of graph, where velocity is plotted on the y-axis and time is plotted on the x-axis.

Q2 → What does the gradient of a velocity–time graph represent?
The gradient (steepness) of a velocity–time graph represents the acceleration of the object. This is because acceleration is defined as the change in velocity divided by time.

Q3 → Why does the gradient equal acceleration?
Acceleration is defined as the change in velocity divided by time. The gradient of a graph is calculated as change in the y-axis value divided by change in the x-axis value. On a velocity–time graph, the y-axis is velocity and the x-axis is time, so the gradient equals acceleration.

Q4 → What does the steepness of a velocity–time graph tell you?
The steeper the graph, the greater the acceleration or deceleration. This means that a larger gradient (positive or negative) indicates a greater rate of change of velocity.

Q5 → What does a flat horizontal line on a velocity–time graph represent?
A flat horizontal line (gradient = 0) represents constant speed. Since the gradient is zero, the acceleration is zero. This means the velocity is constant and not changing.

Q6 → What does a straight line that is not horizontal represent on a velocity–time graph?
A straight line that is not horizontal represents constant acceleration or constant deceleration. This is because the gradient is constant (unchanging), so the acceleration is constant.

Q7 → What does a curved line represent on a velocity–time graph?
A curved line represents changing acceleration or changing deceleration. This means the gradient is not constant, so the acceleration is changing.

Q8 → What does it mean if a curved line is getting steeper?
If a curved line is getting steeper, the gradient is increasing. This means the acceleration is increasing.

Q9 → What does it mean if a curved line is becoming less steep?
If a curved line is becoming less steep, the gradient is decreasing. This means the acceleration is decreasing.

Q10 → What does a positive gradient show on a velocity–time graph?
A positive gradient (an uphill section /) shows that the velocity is increasing and the acceleration is positive.

Q11 → What does a negative gradient show on a velocity–time graph?
A negative gradient (a downhill section ) shows that the velocity is decreasing and the acceleration is negative. This means the object is decelerating.

Q12 → What does a horizontal line on the x-axis represent?
A horizontal line on the x-axis means the velocity equals zero and the gradient is zero. This shows that the object is stationary (at rest) and the acceleration is zero.

Q13 → In GCSE velocity–time graph questions, how should velocity be interpreted?
Velocity includes both speed and direction. However, at GCSE level, velocity–time graphs only cover straight-line motion, so a horizontal line usually implies constant speed because the direction is not changing. You should only refer to velocity (including direction) if the question specifically mentions direction, such as travelling backwards at constant speed (where velocity would be negative but constant).

Q14 → In curved motion, how can speed and velocity differ? (Context clarification)
In curved paths, such as circular motion, speed can remain constant while velocity changes because the direction changes. However, GCSE velocity–time graphs only cover straight-line motion, so this situation is not usually considered unless direction is specifically mentioned.

Q15 → How can acceleration be calculated from a velocity–time graph?
Acceleration can be calculated using the formula:
Acceleration = Change in velocity ÷ Time

This is found by calculating the gradient of the graph.

Q16 → Example: How is acceleration calculated in a straight-line section where velocity changes by 20 m/s in 4 s?
Acceleration = Change in velocity ÷ Time
Acceleration = 20 ÷ 4 = 5 m/s²

Since the line is straight and increasing, the object is travelling at a constant acceleration of 5 m/s².

Q17 → What does a flat horizontal section at 20 m/s for 2 seconds represent?
A flat horizontal section at 20 m/s for 2 seconds represents constant speed of 20 m/s for that 2-second time interval. The gradient is zero, so the acceleration is zero.

Q18 → Example: How is acceleration calculated when velocity changes by 70 m/s between 16 s and 22 s?
Acceleration = Change in velocity ÷ Time
Acceleration = 70 ÷ (22 − 16) = 70 ÷ 6 = 11.7 m/s²

Because the line slopes downwards, the velocity is decreasing. This means the acceleration is negative, so the value is −11.7 m/s². This shows the object is decelerating at a constant rate.

Q19 → What does Section A (positive gradient) represent on a velocity–time graph?
Section A has a positive gradient, meaning the velocity is increasing and the acceleration is positive.

Q20 → What does Section B (zero gradient) represent on a velocity–time graph?
Section B has a zero gradient, indicating that the velocity is constant and the acceleration is zero.

Q21 → What does Section C (negative gradient) represent on a velocity–time graph?
Section C has a negative gradient, signifying that the velocity is decreasing and the acceleration is negative.

Q22 → What does Section D (velocity equals zero and gradient equals zero) represent?
In Section D, the velocity equals zero and the gradient is zero. This means the object is stationary (at rest) and the acceleration is zero.

Q23 → How can you find the acceleration at a particular point on a curved velocity–time graph?
If the graph is curved, you can draw a tangent (a straight line that just touches the curve at that point) and calculate the gradient of the tangent. The gradient of the tangent gives the acceleration at that specific time.

Q24 → What does the area under a velocity–time graph represent?
The area under any section of a velocity–time graph (or the entire graph) represents the distance travelled during that time interval.

Q25 → How can displacement be calculated from a velocity–time graph? (Higher tier)
The displacement of an object can be calculated from the area under a velocity–time graph.

Q26 → How can the area under a velocity–time graph be calculated when the lines are straight?
If the lines are straight, the area under the graph can be calculated using geometry, for example by calculating the area of triangles, rectangles, or trapeziums.

Q27 → How can the area under a curved velocity–time graph be calculated?
If the section under the graph is irregular or curved, it is easier to estimate the area by counting the squares beneath the line and multiplying the number of squares by the value of one square. This method is particularly useful for curved lines.

Answer 1

Source 1: Velocity-Time Graphs
If an object moves along a straight line, the velocity it travels at can be represented by a velocity–time graph: The GRADIENT (steepness) of the line tells you the ACCELERATION of the object. The STEEPER the line, the GREATER the ACCELERATION.

Different features on a velocity-time graph can tell you different information about how an object is travelling: On a velocity-time graph, a flat horizontal line (gradient = 0) indicates constant speed. A straight line that is not horizontal represents constant acceleration or deceleration. A curved line signifies changing acceleration or deceleration. A negative gradient indicates deceleration. A horizontal line on the x-axis (so when velocity=0 and gradient = 0) shows that the object is stationary. (Note that Velocity includes both speed and direction . While a horizontal line does imply constant velocity in straight-line motion (since direction isn’t changing), the specification simplifies this to constant speed for GCSE-level analysis.
In curved paths (e.g., circular motion), speed can be constant while velocity changes (due to changing direction), but velocity-time graphs in the specification only cover straight-line motion, so Only mention velocity if the question specifically references direction (e.g., “travelling backwards” at constant speed, where velocity is negative but constant).) ||| We can use this information to describe the motion of an object with an example of a velocity-time graph: Section 1:
A STRAIGHT LINE means the object is travelling at a CONSTANT ACCELERATION. You can calculate the acceleration by using the equation:

Acceleration = Change in velocity/Time = 20/4 = 5m/s2

Section 2:
A FLAT HORIZONTAL line means the object is travelling at a CONSTANT SPEED of 20m/s for 2s.

Section 3:
The CURVED line is getting STEEPER, which means the GRADIENT is INCREASING.

This means the ACCELERATION is INCREASING.

Section 4:
The CURVED line is getting LESS STEEP, which means the GRADIENT is DECREASING.

This means the ACCELERATION is DECREASING.

Section 5:
The STRAIGHT LINE means the object is travelling at a CONSTANT ACCELERATION. You can calculate the acceleration by using the equation:

acceleration = change in velocity/time = 70/22-16 = 11.7m/s2

The fact that the line goes DOWNWARDS, tells you the VELOCITY IS DECREASING, meaning the object is DECELERATING.

This means the acceleration is NEGATIVE so the value is -11.7m/s2.

Using Tangents
CURVED LINES on velocity-time graphs mean the object has a CHANGING ACCELERATION or DECELERATION.

You can work out its ACCELERATION at a particular time by drawing a TANGENT and finding its GRADIENT.

The Area Under the Graph:
You can find the DISTANCE travelled by an object by working out the AREA UNDER THE GRAPH. ////////// Source 2: Velocity-time graphs:
Determining acceleration:
If an object moves along a straight line, its motion can be represented by a velocity-time graph. The gradient of the line is equal to the acceleration of the object. ||| The following shows what each section of the graph represents:
In Section A, the graph has a positive gradient, which means the velocity is increasing and the acceleration is positive.
In Section B, the gradient is zero, indicating that the velocity is constant and the acceleration is zero.
In Section C, the graph shows a negative gradient, signifying that the velocity is decreasing and the acceleration is negative.
In Section D, where the velocity ( v) equals zero, the gradient is zero, meaning the object is stationary (at rest) and the acceleration is zero. ||| Calculating displacement - higher:
The displacement of an object can be calculated from the area under a velocity-time graph.
The area under the graph can be calculated by:

using geometry (if the lines are straight)
counting the squares beneath the line (particularly if the lines are curved) ////////// Source 3: How an object’s velocity changes as it travels can be plotted on a velocity-time graph.
1) Gradient = acceleration, since acceleration is change in velocity + time.
2) Flat sections represent travelling at a steady speed.
3) The steeper the graph, the greater the
acceleration or deceleration.
4) Uphill sections (/) are acceleration.
5) Downhill sections (\ are deceleration.
6) A curve means changing acceleration.
If the graph is curved, you can use a tangent to the curve
at a point to find the acceleration at that point.
7) The area under any section of the graph (or all of it) is equal to the distance travelled in that time interval.
8) If the section under the graph is irregular, it’s easier to find the area by counting the
squares under the line and multiplying the humber by the value of one square.

Question 2

Q1 → What is a velocity–time graph and what does it show?

Question 3

A velocity–time graph shows how an object’s velocity changes as it travels over time. If an object moves along a straight line

Answer 3

its motion can be represented using this type of graph

Question 4

Q2 → What does the gradient of a velocity–time graph represent?

Question 5

The gradient (steepness) of a velocity–time graph represents the acceleration of the object. This is because acceleration is defined as the change in velocity divided by time.

Question 6

Q3 → Why does the gradient equal acceleration?

Question 7

Acceleration is defined as the change in velocity divided by time. The gradient of a graph is calculated as change in the y-axis value divided by change in the x-axis value. On a velocity–time graph

Answer 7

the y-axis is velocity and the x-axis is time

Question 8

Q4 → What does the steepness of a velocity–time graph tell you?

Question 9

The steeper the graph

Answer 9

the greater the acceleration or deceleration. This means that a larger gradient (positive or negative) indicates a greater rate of change of velocity.

Question 10

Q5 → What does a flat horizontal line on a velocity–time graph represent?

Question 11

A flat horizontal line (gradient = 0) represents constant speed. Since the gradient is zero

Answer 11

the acceleration is zero. This means the velocity is constant and not changing.

Question 12

Q6 → What does a straight line that is not horizontal represent on a velocity–time graph?

Question 13

A straight line that is not horizontal represents constant acceleration or constant deceleration. This is because the gradient is constant (unchanging)

Answer 13

so the acceleration is constant.

Question 14

Q7 → What does a curved line represent on a velocity–time graph?

Question 15

A curved line represents changing acceleration or changing deceleration. This means the gradient is not constant

Answer 15

so the acceleration is changing.

Question 16

Q8 → What does it mean if a curved line is getting steeper?

Question 17

If a curved line is getting steeper

Answer 17

the gradient is increasing. This means the acceleration is increasing.

Question 18

Q9 → What does it mean if a curved line is becoming less steep?

Question 19

If a curved line is becoming less steep

Answer 19

the gradient is decreasing. This means the acceleration is decreasing.

Question 20

Q10 → What does a positive gradient show on a velocity–time graph?

Question 21

A positive gradient (an uphill section /) shows that the velocity is increasing and the acceleration is positive.

Question 22

Q11 → What does a negative gradient show on a velocity–time graph?

Question 23

A negative gradient (a downhill section ) shows that the velocity is decreasing and the acceleration is negative. This means the object is decelerating.

Question 24

Q12 → What does a horizontal line on the x-axis represent?

Question 25

A horizontal line on the x-axis means the velocity equals zero and the gradient is zero. This shows that the object is stationary (at rest) and the acceleration is zero.

Question 26

Q13 → In GCSE velocity–time graph questions

Answer 26

how should velocity be interpreted?

Question 27

Velocity includes both speed and direction. However

Answer 27

at GCSE level

Question 28

Q14 → In curved motion

Answer 28

how can speed and velocity differ? (Context clarification)

Question 29

In curved paths

Answer 29

such as circular motion

Question 30

Q15 → How can acceleration be calculated from a velocity–time graph?

Question 31

Acceleration can be calculated using the formula:

Question 32

Acceleration = Change in velocity ÷ Time

Question 33

This is found by calculating the gradient of the graph.

Question 34

Q16 → Example: How is acceleration calculated in a straight-line section where velocity changes by 20 m/s in 4 s?

Question 35

Acceleration = Change in velocity ÷ Time

Question 36

Acceleration = 20 ÷ 4 = 5 m/s²

Question 37

Since the line is straight and increasing

Answer 37

the object is travelling at a constant acceleration of 5 m/s².

Question 38

Q17 → What does a flat horizontal section at 20 m/s for 2 seconds represent?

Question 39

A flat horizontal section at 20 m/s for 2 seconds represents constant speed of 20 m/s for that 2-second time interval. The gradient is zero

Answer 39

so the acceleration is zero.

Question 40

Q18 → Example: How is acceleration calculated when velocity changes by 70 m/s between 16 s and 22 s?

Question 41

Acceleration = Change in velocity ÷ Time

Question 42

Acceleration = 70 ÷ (22 − 16) = 70 ÷ 6 = 11.7 m/s²

Question 43

Because the line slopes downwards

Answer 43

the velocity is decreasing. This means the acceleration is negative

Question 44

Q19 → What does Section A (positive gradient) represent on a velocity–time graph?

Question 45

Section A has a positive gradient

Answer 45

meaning the velocity is increasing and the acceleration is positive.

Question 46

Q20 → What does Section B (zero gradient) represent on a velocity–time graph?

Question 47

Section B has a zero gradient

Answer 47

indicating that the velocity is constant and the acceleration is zero.

Question 48

Q21 → What does Section C (negative gradient) represent on a velocity–time graph?

Question 49

Section C has a negative gradient

Answer 49

signifying that the velocity is decreasing and the acceleration is negative.

Question 50

Q22 → What does Section D (velocity equals zero and gradient equals zero) represent?

Question 51

In Section D

Answer 51

the velocity equals zero and the gradient is zero. This means the object is stationary (at rest) and the acceleration is zero.

Question 52

Q23 → How can you find the acceleration at a particular point on a curved velocity–time graph?

Question 53

If the graph is curved

Answer 53

you can draw a tangent (a straight line that just touches the curve at that point) and calculate the gradient of the tangent. The gradient of the tangent gives the acceleration at that specific time.

Question 54

Q24 → What does the area under a velocity–time graph represent?

Question 55

The area under any section of a velocity–time graph (or the entire graph) represents the distance travelled during that time interval.

Question 56

Q25 → How can displacement be calculated from a velocity–time graph? (Higher tier)

Question 57

The displacement of an object can be calculated from the area under a velocity–time graph.

Question 58

Q26 → How can the area under a velocity–time graph be calculated when the lines are straight?

Question 59

If the lines are straight

Answer 59

the area under the graph can be calculated using geometry

Question 60

Q27 → How can the area under a curved velocity–time graph be calculated?

Question 61

If the section under the graph is irregular or curved

Answer 61

it is easier to estimate the area by counting the squares beneath the line and multiplying the number of squares by the value of one square. This method is particularly useful for curved lines.