Motion at Constant Acceleration Question 2

In summary, the problem is asking for the length of a runway needed for a light plane to reach a speed of 33 m/s with a constant acceleration of 3.0m/s^2. By using the kinematic equation vf^2 = Vi^2 + 2ad, where vf is the final velocity, Vi is the initial velocity (which is assumed to be 0), a is the acceleration, and d is the displacement, the solution is found to be 1.8m.
  • #1
Adrianna
13
0

Homework Statement


A light plane must reach a speed of 33 m/s for takeoff. How long a runway is needed if the (constant) acceleration is 3.0m/s^2?


Homework Equations


I looked at the Kinematics Equations and tried to re-arrange them to be able to find the distance with what I was given.


The Attempt at a Solution


I am not sure how to start it, this is always my problem I can't seem to figure out what formula to use.
 
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  • #2
Adrianna said:

Homework Statement


A light plane must reach a speed of 33 m/s for takeoff. How long a runway is needed if the (constant) acceleration is 3.0m/s^2?


The Attempt at a Solution


I am not sure how to start it, this is always my problem I can't seem to figure out what formula to use.

You have a final velocity, an initial velocity (the plane should be at rest) and an acceleration. You want to find a displacement.

Which of the kinematic equation contains those 4 quantities?
 
  • #3
vf^2 = Vi^2 +2ad...?
 
  • #4
Adrianna said:
vf^2 = Vi^2 +2ad...?

So when you use that, what do you get for 'd'?
 
  • #5
v^2 = 0 * 2as
where v is final velocity, a is acceleration and s is the distance
 
  • #6
I got 1.8 m/s and that's the right answer thanks so much for the help
 
  • #7
Adrianna said:
I got 1.8 m/s and that's the right answer thanks so much for the help

you mean you got 1.8m. m/s are the units for velocity.
 

What is motion at constant acceleration?

Motion at constant acceleration refers to the movement of an object at a steady rate of change in velocity. This means that the object is accelerating at a constant rate, either increasing or decreasing its velocity by the same amount over equal intervals of time.

What is the difference between constant acceleration and uniform motion?

The main difference between constant acceleration and uniform motion is that in constant acceleration, the velocity is changing at a steady rate, while in uniform motion, the velocity remains constant. In other words, in uniform motion, there is no acceleration.

How is acceleration calculated in motion at constant acceleration?

The acceleration in motion at constant acceleration can be calculated using the formula a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time. This formula can also be rearranged to solve for any of the variables.

What is the relationship between acceleration and force in motion at constant acceleration?

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that a greater force will result in a greater acceleration, while a greater mass will result in a smaller acceleration.

What are some real-life examples of motion at constant acceleration?

Some real-life examples of motion at constant acceleration include a car accelerating from a stop, a ball rolling down a hill, and a rocket launching into space. These all involve a steady change in velocity over time, resulting in constant acceleration.

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