Kinematic Equation in C Programming: Calculate Distance Using d = ut + ½at²

This formula is commonly taught in high school physics and widely used in simulations, robotics, and game development. Today, we’ll apply this concept using a simple C program.

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What Is the Kinematic Equation d = ut + ½at²?

The equation: d=ut+12at2d = ut + \frac{1}{2} a t^2

calculates the distance d travelled by an object with:

• u = initial velocity (m/s)
• a = acceleration (m/s²)
• t = time (s)

It’s a standard kinematic equation used in C programming when simulating motion.

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Implementing the Kinematic Equation in C

Here’s how you can write a C program to apply this formula:

#include <stdio.h>

int main() {
    float u, a, t, d;

    // Input from the user
    printf("Enter initial velocity (u in m/s): ");
    scanf("%f", &u);

    printf("Enter acceleration (a in m/s^2): ");
    scanf("%f", &a);

    printf("Enter time (t in seconds): ");
    scanf("%f", &t);

    // Applying the kinematic equation
    d = u * t + 0.5 * a * t * t;

    // Output the result
    printf("Distance travelled: %.2f meters\n", d);

    return 0;
}

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Sample Output

Input:
u = 10 m/s, a = 2 m/s², t = 5 seconds
Output:
Distance travelled: 75.00 meters

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Real-World Use of Kinematic Equation in C Programming

Using the kinematic equation in C programming is common in:

• Game physics engines
• Autonomous vehicle simulations
• Educational physics software
• Robotics and AI-based motion prediction

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Adding Visual Understanding

Here’s a visual representation of motion with velocity and acceleration:

Image Suggestion: (Insert an image of a motion graph or velocity-time chart with displacement area highlighted)
[Use an open-source or self-made image to avoid copyright issues.]

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Summary

• We used the kinematic formula d = ut + ½at² in a C program.
• The formula calculates distance from velocity, acceleration, and time.
• This logic is foundational in many real-world programming problems involving motion.

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