Speed, Displacement, and Velocity (Leaving Cert Physics): Revision Notes
Velocity
What is velocity?
Velocity is a fundamental concept in physics that describes how quickly an object changes its position in a specific direction. Unlike speed, which only tells us how fast something is moving, velocity gives us both the rate of motion and the direction of movement.
Velocity is defined as the rate of change of displacement with respect to time. This means velocity measures how much an object's position changes over a given time period, taking into account the direction of that change.
The key distinction between speed and velocity is crucial: speed is a scalar quantity (magnitude only), while velocity is a vector quantity (magnitude and direction). This means two objects can have the same speed but different velocities if they're moving in different directions.
Key characteristics of velocity:
- It is a vector quantity, meaning it has both magnitude (size) and direction
- The standard symbol for velocity is v (or sometimes u for initial velocity)
- The unit of velocity is metres per second (m s⁻¹ or m/s)
Average velocity
When an object moves from one position to another, we can calculate its average velocity using either of these equivalent formulas:
or
These two definitions are equivalent because "distance travelled in a given direction" is exactly what displacement means. This relationship highlights why velocity is so closely connected to the concept of displacement rather than just distance.
Worked Example: Calculating Average Velocity
If a car travels 60 metres north in 3 seconds, its average velocity would be:
Notice how the direction (north) is essential to the complete answer.
Constant velocity
An object has constant velocity when specific conditions are met throughout its motion:
- It does not speed up
- It does not slow down
- It does not change direction
- Its average velocity remains the same regardless of the time interval measured
When an object moves in a straight line without speeding up or slowing down, it has constant velocity.
This type of motion is relatively rare in everyday life because friction and other forces typically cause objects to change their motion over time.
Instantaneous velocity refers to an object's velocity at a specific moment in time. For objects with constant velocity, the instantaneous velocity equals the average velocity at all times.
Varying velocity
If a moving object does not have constant velocity, it is said to have varying velocity. This occurs when the object changes its speed, direction, or both during motion.
Common examples of varying velocity include:
- A stone falling towards Earth's surface, which moves in a straight line but with increasing speed due to gravitational acceleration
- An object moving in a circular path at steady speed - even though the speed stays constant, the velocity varies because the direction continuously changes
The key point to remember is that because velocity is a vector quantity, any change in either speed or direction results in varying velocity. This is why an object moving in a circle at constant speed still has varying velocity - the direction is constantly changing.
Measuring velocity in the laboratory
Physicists have developed several methods to accurately measure velocity in controlled laboratory conditions. These methods help us understand motion and verify theoretical predictions.
Ticker tape method
The ticker tape method uses a device called a ticker timer connected to a thin strip of paper tape. Here's how it works:
- A ticker timer operates on a 50 Hz AC source, creating dots on the tape every 1/50th of a second
- The tape is attached to a moving trolley, so when the trolley moves, it pulls the tape through the timer
- The spacing between dots on the tape reveals information about the trolley's motion
Interpreting Ticker Tape Patterns:
- Evenly spaced dots indicate constant velocity - the trolley travelled equal distances in equal time intervals
- Dots getting closer together show the trolley was slowing down (decelerating)
- Dots getting further apart indicate the trolley was speeding up (accelerating)
To calculate velocity from ticker tape:
Since each space represents 1/50 second (0.02 s), you can easily determine the velocity by measuring the distance between consecutive dots.
Linear air track method
The linear air track provides an almost friction-free environment for studying motion. This sophisticated apparatus consists of:
-
A long, rigid tube with holes along its upper surface
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An air blower that forces air through these holes, creating a cushion of air
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A lightweight rider (cart) that floats on this air cushion
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A light gate system for precise measurement
How the Light Gate Works:
- A beam of light shines from a bulb through holes in a stand to reach a photodiode sensor
- When the moving rider interrupts this light beam, the photodiode triggers a scalar timer
- By measuring the time taken for the rider to pass through the light beam, and knowing the length of the card attached to the rider, you can calculate velocity
Velocity calculation with light gates:
Since the time interval measured is very small, this gives a value very close to the instantaneous velocity of the rider at the moment it passes through the light gate.
The beauty of this system is that friction is virtually eliminated, allowing objects to move with true constant velocity once given an initial push. This makes it ideal for studying the fundamental principles of motion without the complications introduced by friction.
Key Points to Remember:
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Velocity is the rate of change of displacement with respect to time - it combines both speed and direction information
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Velocity is a vector quantity measured in metres per second (m s⁻¹), requiring both magnitude and direction to be fully described
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Constant velocity means no change in speed or direction, while varying velocity involves changes in either speed, direction, or both
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Laboratory measurement methods like ticker tape and light gates allow precise velocity measurements by tracking motion over known time intervals
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The distinction between speed and velocityis crucial - speed is scalar (magnitude only), while velocity is vector (magnitude and direction)