Forces & Motion
Speed, Velocity and Acceleration
1st Year · 2nd Year · 3rd Year (Junior Cert)
- ✓By the end of this lesson students will be able to define and distinguish between distance and displacement, and speed and velocity.
- ✓By the end of this lesson students will be able to interpret and draw distance-time graphs to describe motion.
- ✓By the end of this lesson students will be able to interpret and draw speed-time graphs to describe motion and calculate distance travelled.
- ✓By the end of this lesson students will be able to understand and apply the word-level equations for speed, velocity, and acceleration.
Key concepts
Distance is the total length of the path travelled by an object. It is a scalar quantity, meaning it only has magnitude (size) and no direction.
Displacement is the straight-line distance from the starting point to the ending point, in a specified direction. It is a vector quantity, meaning it has both magnitude and direction.
Speed is the rate at which an object covers distance. It is a scalar quantity. The average speed is calculated by dividing the total distance travelled by the total time taken.
Velocity is the rate at which an object changes its displacement. It is a vector quantity. The average velocity is calculated by dividing the total displacement by the total time taken.
Acceleration is the rate at which an object's velocity changes. This change can be in speed, direction, or both. It is a vector quantity. An object accelerates if it speeds up, slows down (decelerates), or changes direction.
A distance-time graph shows how an object's distance from a starting point changes over time. - A horizontal line means the object is stationary (not moving). - A straight line sloping upwards means the object is moving at a constant speed. A steeper slope indicates a greater speed. - A curved line means the object's speed is changing (it is accelerating or decelerating).
A speed-time graph shows how an object's speed changes over time. - A horizontal line means the object is moving at a constant speed (zero acceleration). - A straight line sloping upwards means the object is accelerating at a constant rate. A steeper slope indicates a greater acceleration. - A straight line sloping downwards means the object is decelerating (negative acceleration) at a constant rate. - The area under a speed-time graph represents the total distance travelled by the object.
Key facts to remember
- 1Distance is a scalar quantity (magnitude only); displacement is a vector quantity (magnitude and direction).
- 2Speed is the rate of change of distance; velocity is the rate of change of displacement.
- 3Acceleration is the rate of change of velocity.
- 4On a distance-time graph, the gradient (slope) of the line represents the speed.
- 5On a speed-time graph, the gradient (slope) of the line represents the acceleration.
- 6On a speed-time graph, the area under the graph represents the total distance travelled.
- 7The standard units are: distance (metres, m), time (seconds, s), speed/velocity (metres per second, m/s), and acceleration (metres per second squared, m/s²).
Worked examples
Example 1
A cyclist travels a distance of 1800 metres in 5 minutes. Calculate the average speed of the cyclist in metres per second (m/s).
Answer
The average speed of the cyclist is 6 m/s.
Always ensure your units are consistent before performing calculations.
Example 2
The following data describes the motion of a car: - From 0 s to 10 s, the car travels 50 m. - From 10 s to 20 s, the car remains stationary at 50 m from the start. - From 20 s to 30 s, the car travels another 100 m, reaching 150 m from the start. Describe the motion of the car during each interval and calculate the speed of the car during the first and third intervals.
Answer
Interval 1 (0-10 s): Car moves at a constant speed of 5 m/s. Interval 2 (10-20 s): Car is stationary. Interval 3 (20-30 s): Car moves at a constant speed of 10 m/s.
For distance-time graphs, the slope of the line gives the speed. A horizontal line means zero speed.
Example 3
A bus starts from rest and accelerates uniformly to a speed of 20 m/s in 5 seconds. It then travels at this constant speed for another 10 seconds. Calculate the acceleration of the bus during the first 5 seconds and the total distance travelled by the bus.
Answer
The acceleration of the bus during the first 5 seconds is 4 m/s². The total distance travelled by the bus is 250 m.
For speed-time graphs, the area under the graph represents the distance travelled. Break complex shapes into simpler ones (triangles and rectangles) to find the area.
Common mistakes
- ✗Confusing speed with velocity, or distance with displacement, especially when describing motion.
- ✗Not converting units (e.g., minutes to seconds, km/h to m/s) before performing calculations.
- ✗Incorrectly calculating the gradient of a line on a graph (rise over run).
- ✗Forgetting that a horizontal line on a distance-time graph means stationary, but on a speed-time graph means constant speed.
- ✗Failing to calculate the area under a speed-time graph correctly to find the distance travelled.
Exam tips
- ★Always read the labels on the axes of graphs carefully to determine if it is a distance-time or speed-time graph, as their interpretations are different.
- ★Show all steps in your calculations: write the formula, substitute the values, and state the final answer with correct units.
- ★When describing motion from a graph, use precise terms like 'constant speed', 'accelerating', 'decelerating', or 'stationary'.
- ★Practise drawing and interpreting various types of motion on both distance-time and speed-time graphs to build confidence.
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