What We Review
Introduction
Motion is a fundamental concept in physics that helps us describe how objects move. Whether it’s the movement of a car, a thrown ball, or even a person walking, understanding motion is crucial. The key concepts involved are displacement, velocity, and acceleration. These terms help us understand not just how far or fast something is moving, but also how it changes motion over time.
What is Displacement?
Displacement is the change in an object’s position. It’s not the same as distance. While distance measures how much ground an object covers, displacement focuses on the direct change from the starting point to the ending point. Think of it as the shortest path.
Displacement Formula
The formula for displacement is: \Delta x = x - x_0
Here, \Delta x represents displacement, x is the final position, and x_0 is the starting position.
Example Calculation: Finding Displacement
Scenario: A car moves from position 3 meters to 10 meters on a straight road.
Steps:
- Identify the initial position, x_0 = 3 \mathrm{\ m}.
- Identify the final position, x = 10 \mathrm{\ m}.
- Apply the displacement formula:
Thus, the car’s displacement is 7 meters.
Understanding Velocity
Velocity is a vector quantity that refers to the rate at which an object changes its position. Unlike speed, which is scalar and only considers how fast an object is moving, velocity includes direction.
Velocity Formula
The formula for average velocity is: \vec{v}_{avg} = \frac{\Delta \vec{x}}{\Delta t}
Where \vec{v}_{avg} is the average velocity, \Delta \vec{x} is the displacement, and \Delta t is the time taken.
Example Calculation: Finding Average Velocity
Scenario: A runner completes a 400-meter lap in 50 seconds.
Steps:
- Find the displacement: \Delta \vec{x} = 400 \mathrm{\ m}.
- Time taken: \Delta t = 50 \mathrm{\ s}.
- Use the velocity formula:
So, the average velocity of the runner is 8 meters per second.
Decoding Acceleration
Acceleration describes how velocity changes over time. If an object speeds up, slows down, or changes direction, it’s accelerating.
Acceleration Formula
The formula for average acceleration is: \vec{a} = \frac{\Delta \vec{v}}{\Delta t}
Here, \vec{a} represents the acceleration, \Delta \vec{v} is the change in velocity, and \Delta t is the time interval.
Example Calculation: Finding Average Acceleration
Scenario: A car accelerates from rest to 20 meters per second in 5 seconds.
Steps:
- Initial velocity, \vec{v}_0 = 0 \mathrm{\ m/s} (since it starts at rest).
- Final velocity, \vec{v} = 20 \mathrm{\ m/s}.
- Time interval, \Delta t = 5 \mathrm{\ s}.
- Use the acceleration formula:
Therefore, the car’s average acceleration is 4 \mathrm{\ m/s^2}.
Relationship Between Displacement, Velocity, and Acceleration
These concepts are deeply connected. Displacement tells us where an object goes, velocity tells us how fast it gets there and in what direction, and acceleration explains changes in velocity over time. For example, when driving a car, pressing the gas pedal changes its speed, thus changing its velocity and causing acceleration. For more review and examples, try out video guides such as Flipping Physics.
Summary and Key Takeaways of Displacement, Velocity, and Acceleration
- Displacement is the change in position: \Delta x = x - x_0.
- Velocity is the rate of change of displacement, and it includes direction: \vec{v}_{avg} = \frac{\Delta \vec{x}}{\Delta t}.
- Acceleration is the rate of change of velocity: \vec{a} = \frac{\Delta \vec{v}}{\Delta t}.
Understanding these three helps predict motion and analyze various real-world scenarios. Practice is key to mastering these concepts.
Quick Reference Chart for Displacement, Velocity, and Acceleration
| Term | Definition |
| Displacement | Change in an object’s position \Delta x = x - x_0 |
| Velocity | Displacement divided by time \vec{v}_{avg} = \frac{\Delta \vec{x}}{\Delta t} |
| Acceleration | Change in velocity divided by time \vec{a} = \frac{\Delta \vec{v}}{\Delta t} |
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