Distance Formula: Calculate w/ Acceleration & Time

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To calculate distance with constant acceleration and no initial velocity, use the formula d = (1/2)at², where d is distance, a is acceleration, and t is time. This formula derives from integrating acceleration to find velocity and then integrating velocity to find position. For non-constant acceleration, the calculation becomes more complex, typically requiring calculus to integrate the acceleration function over time. The specific formula will depend on the functional form of the acceleration. Understanding these principles is crucial for accurately determining distance in varying scenarios.
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I'm doing a project for a science class and need to know how you calculate distance when given acceleration and time (with no beginning velocity).
 
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Assuming you are talking about a constant acceleration, what you are looking for is

<br /> d=\frac{1}{2}at^2+v_0 t<br />

where d is the total distance traveled, a is the acceleration, v_0 is the initial velocity but you said you will be taking that as zero. If you know calculus, the way you arrive at this formula comes simply from integrating the constant acceleration twice; in other words, with calculus you can say that the integral of acceleration (where the integration variable is time) is velocity, and the integral of velocity (integration variable also time) is position.
 
16180339887 said:
Assuming you are talking about a constant acceleration, .

just wondering what's the formulae if its not constant
 
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