Distance Formula: Calculate w/ Acceleration & Time

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In summary, the formula for calculating distance when given acceleration and time (with no initial velocity) is d = 1/2 * a * t^2, where d is the total distance traveled, a is the acceleration, and t is the time. This formula can be derived through integration of the constant acceleration formula, and may vary if the acceleration is not constant.
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spencerda
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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

[tex]
d=\frac{1}{2}at^2+v_0 t
[/tex]

where [itex]d[/itex] is the total distance traveled, [itex]a[/itex] is the acceleration, [itex]v_0[/itex] 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.
 
  • #3
16180339887 said:
Assuming you are talking about a constant acceleration, .

just wondering what's the formulae if its not constant
 

FAQ: Distance Formula: Calculate w/ Acceleration & Time

1. What is the distance formula?

The distance formula is a mathematical equation used to calculate the distance between two points in a straight line. It is often used in physics to determine the distance an object has traveled over a period of time.

2. How is acceleration involved in the distance formula?

Acceleration is a measure of change in velocity over time. In the distance formula, it is used to calculate the change in velocity over a specific period of time, thus determining the distance traveled by an object.

3. What is the role of time in the distance formula?

Time is an essential factor in the distance formula as it is used to determine the duration over which an object has traveled at a certain velocity. It is typically represented by the variable "t" in the equation.

4. How do you use the distance formula to calculate an object's distance?

To use the distance formula, you need to know the initial velocity, final velocity, and the time in which the object traveled. You can then plug these values into the equation (d = 1/2 * (v0 + v) * t) and solve for the distance traveled.

5. Can the distance formula be used for objects with varying acceleration?

Yes, the distance formula can be used for objects with varying acceleration. However, in this case, the average acceleration over the given time period should be used in the equation to calculate the distance traveled.

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