Displacement (s) Calculator
Understanding the motion of objects is a fundamental concept in physics and engineering. One of the key quantities used to describe motion is displacement (s). Unlike distance, which is a scalar quantity representing the total path length traveled, displacement is a vector quantity that measures the shortest distance from the initial to the final position of an object, including its direction.
What is Displacement?
Displacement refers to the change in an object's position. If an object starts at point A and moves to point B, its displacement is the straight-line distance and direction from A to B, regardless of the path taken. For example, if you walk 5 meters east, then 5 meters west, your total distance traveled is 10 meters, but your displacement is 0 meters because you ended up at your starting point.
The Kinematic Equation for Displacement
When an object moves with constant acceleration, we can use a set of equations known as the kinematic equations to describe its motion. The calculator above utilizes one of these equations to find displacement (s) when you know the initial velocity (u), the time duration (t), and the constant acceleration (a). The formula is:
s = ut + ½at²
- s: Displacement (measured in meters, m)
- u: Initial Velocity (the velocity of the object at the beginning of the time interval, measured in meters per second, m/s)
- t: Time (the duration over which the motion occurs, measured in seconds, s)
- a: Acceleration (the rate of change of velocity, measured in meters per second squared, m/s²)
How the Calculator Works
This Displacement (s) Calculator simplifies the process of applying the kinematic equation. You simply input the following values:
- Initial Velocity (u): Enter the starting speed and direction of the object.
- Time (t): Input the total time the object is in motion.
- Acceleration (a): Provide the constant rate at which the object's velocity changes.
Once you click "Calculate Displacement," the tool will instantly compute the object's displacement using the formula s = ut + ½at² and display the result in meters.
Example Calculation
Let's consider a car that starts from rest (initial velocity = 0 m/s) and accelerates uniformly at 2 m/s² for 5 seconds.
- Initial Velocity (u) = 0 m/s
- Time (t) = 5 s
- Acceleration (a) = 2 m/s²
Using the formula:
s = (0 m/s * 5 s) + (0.5 * 2 m/s² * (5 s)²)
s = 0 + (1 * 25)
s = 25 meters
So, the car's displacement after 5 seconds would be 25 meters. You can input these values into the calculator to verify the result.