Motion can be analysed mathematically using relationships between distance, time, speed, force and acceleration. Speed is distance divided by time (speed = distance ÷ time); acceleration is the rate at which speed changes over time. Force causes acceleration — Newton's second law states that force equals mass multiplied by acceleration (F = ma), meaning a heavier object needs more force to accelerate at the same rate as a lighter one. These relationships can be represented and analysed using both graphs (like distance-time and speed-time graphs) and algebraic formulas, giving two complementary ways to understand the same motion.
Example
A car accelerating from rest would show a distance-time graph that curves increasingly steeply (since it covers more distance each second as it speeds up), while its corresponding speed-time graph would show a rising line — both graphs represent the exact same motion, just emphasising different aspects of it.
Key terms
Speed:
Distance travelled divided by time taken.
Acceleration:
The rate at which speed changes over time.
Newton's second law:
Force equals mass multiplied by acceleration (F = ma).
Questions
1. Speed is calculated as:
Distance ÷ time
Time ÷ distance
Distance × time
Time − distance
2. Acceleration is:
The rate at which speed changes over time
The same thing as speed
A measure of distance only
Always equal to zero
3. Newton's second law states that force equals:
Mass multiplied by acceleration
Mass divided by acceleration
Mass plus acceleration
Mass minus acceleration
4. A heavier object needing more force to accelerate at the same rate as a lighter one demonstrates:
Newton's second law
A law with no connection to mass
The concept of speed only
A completely random, unrelated fact
5. Motion can be represented using:
Both graphs and algebraic formulas
Only drawings, never numbers
Neither graphs nor formulas
Only spoken descriptions
6. A distance-time graph shows:
How distance changes over time
Only the object's mass
Only the object's colour
Nothing related to motion
7. A speed-time graph shows:
How speed changes over time
Only the object's starting position
Only the object's mass
Nothing related to motion
8. A car travels 150km in 3 hours. What is its average speed?
50 km/h
450 km/h
3 km/h
147 km/h
9. A cyclist accelerates from 0 to 10 m/s in 5 seconds. What is their acceleration?
2 m/s²
50 m/s²
5 m/s²
10 m/s²
10. A 10kg object needs a force to accelerate at 3 m/s². Using F = ma, what force is required?
30 N
13 N
3.3 N
7 N
11. On a distance-time graph, a straight, sloped line (rather than a curve) represents:
Constant speed
Constant acceleration
No motion at all
Random, unpredictable motion
12. On a distance-time graph, a horizontal (flat) line represents:
The object being stationary
The object moving at maximum speed
The object accelerating rapidly
A graphing error
13. Why does a steeper line on a distance-time graph indicate a faster speed?
A steeper slope means more distance is covered in the same amount of time
The steepness of a distance-time graph has no connection to speed
A steeper line always indicates the object has stopped moving
Slope on a distance-time graph only ever represents acceleration, never speed
14. Why might a curved (rather than straight) line on a distance-time graph indicate that an object is accelerating rather than moving at constant speed?
A curve shows the distance covered per unit of time is changing, meaning speed itself is changing, which is the definition of acceleration
A curved line on a distance-time graph always indicates the object has completely stopped moving
Curved and straight lines on a distance-time graph always represent exactly identical types of motion
The shape of a distance-time graph has no connection to whether an object is accelerating
15. Two objects of different mass are pushed with the exact same force. Why does the lighter object accelerate more?
Since force equals mass times acceleration, a smaller mass requires less force to achieve a given acceleration, so the same force produces greater acceleration
Mass has no effect on how much an object accelerates under a given force
The heavier object should always accelerate faster than the lighter one under the same force
Force and acceleration have no mathematical relationship to mass whatsoever
16. A speed-time graph shows a straight line sloping upward at a constant rate. What does this indicate about the object's acceleration?
Constant, unchanging acceleration
Zero acceleration throughout
Acceleration that is constantly changing
The object is not moving at all
17. Why might the area under a speed-time graph represent the total distance travelled?
Multiplying speed by time (which is what area under the graph effectively calculates) gives distance, consistent with the relationship between these quantities
The area under a speed-time graph has no mathematical meaning or connection to distance
Distance can only ever be calculated directly from a distance-time graph, never a speed-time graph
Area under any type of graph always represents acceleration, never distance
18. A rocket increases its force output while its mass decreases as fuel burns off. Using F = ma, why does this combination cause its acceleration to increase especially rapidly?
Increasing force alongside decreasing mass both independently work to increase acceleration, so combined they compound the effect
Decreasing mass always decreases acceleration according to F = ma, regardless of force
Force and mass have no combined effect on acceleration beyond their individual, separate effects
A rocket's acceleration is completely unrelated to its changing mass or force output
19. Why is understanding the relationship between force, mass and acceleration essential for engineers designing vehicle safety features like crumple zones?
Crumple zones work by extending the time over which a collision force acts, reducing the acceleration (and therefore force) experienced by passengers
Force, mass and acceleration have no real connection to vehicle safety engineering
Crumple zones function with no relationship to any laws of motion
Vehicle safety design never actually requires any understanding of the physics of motion
20. Why might comparing a distance-time graph and a speed-time graph for the exact same journey reveal different, complementary details about that motion?
Each graph emphasises a different aspect of the same underlying motion — one shows position changing over time, the other shows the rate of that change — so together they give a fuller picture
These two types of graphs always show exactly identical information with no complementary difference between them
Only one of these two graph types can ever be meaningfully used to describe a given journey
The type of graph used to represent motion has no bearing on which specific details are emphasised
21. Understanding motion through speed, force and acceleration mainly helps you to:
Analyse and represent real-world motion using mathematical relationships and graphs
Assume speed and acceleration always mean exactly the same thing
Ignore the relationship between an object's mass and the force needed to accelerate it
Treat graphs and algebraic formulas as unrelated ways of describing the same motion
Answer key (parent copy)
1. Distance ÷ time
2. The rate at which speed changes over time
3. Mass multiplied by acceleration
4. Newton's second law
5. Both graphs and algebraic formulas
6. How distance changes over time
7. How speed changes over time
8. 50 km/h
9. 2 m/s²
10. 30 N
11. Constant speed
12. The object being stationary
13. A steeper slope means more distance is covered in the same amount of time
14. A curve shows the distance covered per unit of time is changing, meaning speed itself is changing, which is the definition of acceleration
15. Since force equals mass times acceleration, a smaller mass requires less force to achieve a given acceleration, so the same force produces greater acceleration
16. Constant, unchanging acceleration
17. Multiplying speed by time (which is what area under the graph effectively calculates) gives distance, consistent with the relationship between these quantities
18. Increasing force alongside decreasing mass both independently work to increase acceleration, so combined they compound the effect
19. Crumple zones work by extending the time over which a collision force acts, reducing the acceleration (and therefore force) experienced by passengers
20. Each graph emphasises a different aspect of the same underlying motion — one shows position changing over time, the other shows the rate of that change — so together they give a fuller picture
21. Analyse and represent real-world motion using mathematical relationships and graphs