Given position and velocity, find acceleration

In summary, an airplane with constant acceleration requires 800 ft. of runway before lifting off at a velocity of 100 ft./sec. The relevant equations for this problem involve integration and the relationship between acceleration, velocity, and time. The student is advised to start by writing down the differential form of this relationship and then applying the Chain Rule to bring displacement into the equation.
  • #1
canadiankeeg
2
0

Homework Statement



An airplane has a constant acceleration while moving down the runway from rest.
What is the acceleration of the plane if it requires 800 ft. of runway before lifting o
at 100 ft./sec.?

Homework Equations





The Attempt at a Solution

 
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  • #2
You have to post your attempt. Start with the equation of motion that's most relevant here.
 
  • #3
sorry, wrong section its for a calculus class and we have to solve by integration and I am not sure where to start.
 
  • #4
canadiankeeg said:
sorry, wrong section its for a calculus class and we have to solve by integration and I am not sure where to start.

OK, then, start by writing down the relationship between acceleration, velocity and time in differential form.

Then apply Chain Rule to bring displacement into there somewhere. There's more to do, but why don't you start with this?
 
  • #5
You are expected to know that velocity is the derivative of position with respect to time and acceleration is the derivative of velocity.
 

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

The formula for finding acceleration is a = (vf - vi)/t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time interval.

2. Can acceleration be negative?

Yes, acceleration can be negative. A negative acceleration means that an object is slowing down or decelerating.

3. How do you find the direction of acceleration?

The direction of acceleration is determined by the direction of the change in velocity. If the velocity is increasing, the acceleration is in the same direction. If the velocity is decreasing, the acceleration is in the opposite direction.

4. Is acceleration constant in all cases?

No, acceleration is not constant in all cases. In some cases, such as freefall or circular motion, acceleration can change over time.

5. How is acceleration related to force?

According to Newton's Second Law of Motion, force is equal to mass times acceleration (F=ma). This means that the greater the force applied to an object, the greater its acceleration will be.

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