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In physics, displacement is defined as the shift in an object's position. For instance, if you travel 1 mile (1.6 kilometers) to your friend's home, the displacement of your car is 1 mile (1.6 kilometers). Marin Tomas / Getty ImagesPhysicists utilize the displacement formula to determine the change in an object's location. Although the idea seems easy, calculating displacement can become intricate quickly.
Let’s simplify this concept with some worked examples.
What Does Displacement Mean?
In the realm of physics, displacement describes the change in an object's position. For instance, if you walk 1 mile (1.6 kilometers) to your friend's place, your displacement is 1 mile (1.6 kilometers).
However, if you walk a 1-mile (1.6-kilometer) circular path that begins and ends at the same point, your displacement would be 0. Likewise, if your friend's home is 1 mile (1.6 kilometers) away, but you take a winding route instead of walking in a straight line, your displacement is still 1 mile (1.6 kilometers).
This is because displacement calculates the shortest distance between the starting and ending points of an object. The specific path taken is irrelevant; displacement always refers to the shortest route between the initial and final positions.
Displacement vs. Distance: What Sets Them Apart?
Distance is the total length of the path that an object travels, whereas displacement is the change in the object's position from the starting point to the final location. Wait, isn't that the same thing?
Only if the object follows the most direct route from point A to point B.
For example, if you walk a 1-mile (1.6-kilometer) circular path, the total distance covered is 1 mile (1.6 kilometers), but the displacement is 0. Keep in mind that displacement is always less than or equal to distance because it represents the straight-line distance between the starting and ending points.
In scientific terms, distance is a scalar quantity, like speed, while displacement is a vector quantity, like velocity. Scalars only have magnitude, whereas vectors have both magnitude and direction.
Displacement Formulas
The fundamental equation for calculating displacement is a rearranged version of the velocity formula:
Here, d represents displacement, v stands for average velocity, and t refers to the time taken to travel from point A to point B.
If the object moves at a constant velocity, finding the displacement is simple. However, if the velocity is not constant, you can calculate displacement by using the initial and final velocities with the acceleration formula. (For situations involving multiple velocities, you might want to consider using displacement calculators available on websites like Omni Calculator and Calculator Soup.)
Applying the Acceleration Formula
If the object you're calculating displacement for experiences constant acceleration, you can apply the acceleration equation, which is derived from Newton's third law of motion:
In this equation, a stands for acceleration, v1 is the initial velocity, v is the final velocity of the object, and t represents the time taken. If you're using this formula to find displacement, the equation becomes:
Where d is the displacement, a is acceleration, t is the time interval from the start to the end point, and v is the final velocity of the object.
Example of Displacement Formula
Let's work through a few real-life situations to calculate displacement.
Scenario 1: Steady Velocity
If an object moves at a constant velocity, you can apply the velocity formula to find its displacement. For instance, if a car is traveling at an average speed of 25 miles per hour (40 kilometers per hour) for 15 minutes, how far would it travel?
We can use the following formula to solve this:
In this case, v represents the speed, which is 25 miles per hour (or 40 kilometers per hour), and t denotes the time, which is 15 minutes, equivalent to 0.25 hours.
Thus, after traveling for 25 minutes at a consistent speed of 25 miles per hour (40 kilometers per hour), the car covers a distance of 6.25 miles (10 kilometers).
Example 2: Uniform Acceleration
If a vehicle moving at 22.4 miles per hour (36 kilometers per hour) needs to stop within 30 seconds, what would be its displacement?
To determine the acceleration, let's start with the following calculation.
Where v1 represents the car's initial speed (22.4 miles per hour or 36 kilometers per hour), v is its final velocity (0 miles per hour), and t is the time (30 seconds).
To begin with, we need to perform some unit conversions to express the acceleration in the proper SI units — meters per second squared.
Now, we can substitute this value directly into the equation.
Now that the acceleration has been determined, we can proceed to calculate the displacement.
In this equation, a represents acceleration (0.33 meters per second squared), t stands for time (30 seconds), and v is the final velocity (0 meters per second).
The vehicle traveled a total displacement of 349.005 meters (1,145 feet) before coming to a stop.
