# Translating acceleration into distance traveled

• Spirochete
In summary, when calculating the distance traveled by an object with a constant acceleration starting from 0 velocity for a known period of time, the equations used are s=v_{0}t + \frac{at^{2}}{2} and v_{1}^{2}-v_{0}^{2}=2as, where v_{0} is the initial velocity, a is the acceleration, t is the time elapsed, and s is the distance traveled. These equations are derived from Newton's equations of motion and are used in cases of uniform motion.

## Homework Statement

If something is moving at a constant acceleration (starting from 0 velocity) for a known period of time, how do you figure how far they've traveled? Eg. a car is accelerating at 2 m/s^2 for 20 seconds.

I'm taking an algebra based physics course.

## Homework Equations

I do not know which equation are relevant.

## The Attempt at a Solution

I know I can multiply time by acceleration and get a final velocity. for example the final velocity is 40 m/s in my example. I don't know how to factor position into it.

Look up Newton's equations of motion

I can tell you how to derive them if you wish.

Hello,

I think the equations you need are those we use for uniform motion, ie when the acceleration is constant.

Assuming all the motion is one direction only the distance traveled will be $$s=v_{0}t + \frac{at^{2}}{2}$$

where $$v_{0}=initial\ velocity\; a=acceleration\; t=time\ elapsed\; and\ s=distance\ traveled$$

Also $$v_{1}^{2}-v_{0}^{2}=2as$$

Vuldoraq said:
Hello,

I think the equations you need are those we use for uniform motion, ie when the acceleration is constant.

Assuming all the motion is one direction only the distance traveled will be $$s=v_{0}t + \frac{at^{2}}{2}$$

where $$v_{0}=initial\ velocity\; a=acceleration\; t=time\ elapsed\; and\ s=distance\ traveled$$

Also $$v_{1}^{2}-v_{0}^{2}=2as$$

Thanks that works

## 1. How is acceleration related to distance traveled?

Acceleration is the rate of change of velocity over time. This means that as acceleration increases, so does the change in velocity. Since distance is the product of velocity and time, an increase in acceleration will result in a greater distance traveled.

## 2. What units are used to measure acceleration and distance?

Acceleration is typically measured in meters per second squared (m/s^2), while distance is measured in meters (m). However, other units such as miles per hour squared (mi/h^2) and feet (ft) may also be used depending on the context.

## 3. Can acceleration be negative when calculating distance traveled?

Yes, acceleration can be negative when calculating distance traveled. This simply means that the object is decelerating or slowing down. The negative sign indicates that the direction of acceleration is opposite to the direction of motion.

## 4. How can I calculate the distance traveled from a given acceleration?

To calculate the distance traveled from a given acceleration, you can use the equation d = (1/2)at^2, where d is the distance, a is the acceleration, and t is the time elapsed. This equation is derived from the average velocity formula, v = d/t, and the definition of acceleration, a = (vf - vi)/t.

## 5. Are there any other factors that affect the distance traveled besides acceleration?

Yes, besides acceleration, the initial velocity and time also affect the distance traveled. The higher the initial velocity, the greater the distance traveled. Similarly, the longer the time, the greater the distance traveled. Additionally, factors such as air resistance, friction, and the shape of the object can also impact the distance traveled.