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Distance Under Constant Acceleration Formula:
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The distance under constant acceleration formula calculates the total distance traveled by an object when it starts with an initial velocity and experiences constant acceleration over time. This fundamental physics equation is essential for motion analysis in kinematics.
The calculator uses the distance formula:
Where:
Explanation: The formula consists of two parts - the distance covered due to initial velocity (\( v_i t \)) and the additional distance due to acceleration (\( \frac{1}{2} a t^2 \)).
Details: Accurate distance calculation under acceleration is crucial for physics problems, engineering applications, vehicle dynamics, projectile motion analysis, and understanding motion in various scientific fields.
Tips: Enter initial velocity in m/s, acceleration in m/s², and time in seconds. Time must be positive. All values can be positive, negative, or zero depending on the motion scenario.
Q1: What if initial velocity is zero?
A: If \( v_i = 0 \), the formula simplifies to \( d = \frac{1}{2} a t^2 \), which represents distance from rest under constant acceleration.
Q2: Can acceleration be negative?
A: Yes, negative acceleration indicates deceleration. The object is slowing down, and distance calculation accounts for this reduction in speed.
Q3: What are typical units for this calculation?
A: Standard SI units are meters for distance, m/s for velocity, m/s² for acceleration, and seconds for time. Ensure consistent units for accurate results.
Q4: When is this formula not applicable?
A: This formula assumes constant acceleration. It doesn't apply to variable acceleration scenarios or relativistic speeds where Einstein's equations are needed.
Q5: How does this relate to free fall?
A: For free fall near Earth's surface, acceleration \( a = -9.8 \) m/s² (negative indicates downward direction), and the formula calculates vertical distance.