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Distance Equation:
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The distance equation (d = u t + (1/2) a t²) calculates the distance traveled by an object under constant acceleration. It's a fundamental equation in kinematics that relates initial velocity, time, acceleration, and displacement.
The calculator uses the distance equation:
Where:
Explanation: The equation calculates the total distance traveled by summing the distance due to initial velocity (u t) and the distance due to constant acceleration (½ a t²).
Details: This calculation is essential in physics, engineering, and motion analysis. It helps predict an object's position, plan trajectories, and understand motion dynamics in various applications from vehicle braking to projectile motion.
Tips: Enter initial velocity in m/s, time in seconds, and acceleration in m/s². Time must be positive. All values can be positive, negative, or zero depending on the direction of motion.
Q1: What does negative acceleration mean?
A: Negative acceleration (deceleration) means the object is slowing down in the positive direction or speeding up in the negative direction.
Q2: Can initial velocity be negative?
A: Yes, negative initial velocity indicates motion in the opposite direction of the defined positive direction.
Q3: What if time is zero?
A: If time is zero, the distance traveled will be zero regardless of other values, as no time has passed for motion to occur.
Q4: How is this different from average velocity equations?
A: This equation specifically accounts for constant acceleration, while average velocity equations assume constant speed.
Q5: What are practical applications of this equation?
A: It's used in calculating stopping distances for vehicles, predicting projectile trajectories, designing roller coasters, and analyzing any motion with constant acceleration.