Given acceleration and velocity; find length

In summary, the formula for finding length with given acceleration and velocity is L = v^2 / (2a), where L is the length, v is the velocity, and a is the acceleration. Acceleration affects the length of an object by increasing or decreasing its speed. No, length cannot be negative when using this formula. The units for velocity should be in meters per second (m/s) and the units for acceleration should be in meters per second squared (m/s^2). This formula can be used for any type of motion where there is a constant acceleration, including both linear and circular motion.
  • #1
cassienoelle
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Homework Statement


An aircraft takes off at 213 km/h after accelerating from rest at 2.86 m/s2. What is the minimum runway length required?


Homework Equations





The Attempt at a Solution


I know it's super simple, but I can't figure it out. I know I have to convert 213km/hr to m/s, but then what?
 
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  • #2
List your kinematics equations. Which ones involve acceleration, distance, and velocity? Try to pick one that doesn't need time.
 

1. What is the formula for finding length with given acceleration and velocity?

The formula for finding length with given acceleration and velocity is:
L = v2 / (2a)
where L is the length, v is the velocity, and a is the acceleration.

2. How does acceleration affect the length of an object?

Acceleration affects the length of an object by increasing or decreasing its speed. The greater the acceleration, the greater the change in velocity and therefore the greater the change in length of the object.

3. Can length be negative when using this formula?

No, length cannot be negative when using this formula. This is because both velocity and acceleration are squared in the formula, which means they will always result in a positive value. Therefore, the length calculated will always be positive.

4. What units should be used for velocity and acceleration in this formula?

The units for velocity should be in meters per second (m/s) and the units for acceleration should be in meters per second squared (m/s2). This will ensure that the units for length will be in meters (m).

5. Can this formula be used for any type of motion?

Yes, this formula can be used for any type of motion where there is a constant acceleration. This includes both linear and circular motion, as long as the acceleration remains constant throughout the motion.

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