What is the Acceleration of a Small Body Moving on a Parabola?

In summary, the conversation discusses finding the acceleration for a small body moving in the xy plane with a constant velocity and x=0 for the parabola y=ax^2. The equations and attempt at a solution involve differentiating vectors and determining the magnitude of the acceleration, which is orthogonal to the velocity.
  • #1
GregoryGr
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Homework Statement



a small body is moving in the plane xy with a constant (in size) velocity [ sorry for my english]. Find the acceleration for x=0 for the parabola [tex]y=ax^2[/tex]

Homework Equations





The Attempt at a Solution



[tex] v^2= a_x^2 +a_y^2 \\ \vec{v}= a_x\vec{x}+ a_y*\vec{y}[/tex] and $$\vec{a}=d\vec{v}/dt$$

I'm kind of lost now, mainly because I'm new to differentiating vectors... Any help would be helpful...
 
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  • #2
Constant velocity means that acceleration is 0 or that the direction of velocity is changing, so is the velocity changing direction?
 
  • #3
The magnitude of the velocity is usually called the speed. If the speed is constant then any acceleration is orthogonal to the velocity. So what direction will the acceleration be in at x=0?
It remains to determine the magnitude of the acceleration. By differentiating the equations you have you should be able to determine ##\ddot x^2+ \ddot y^2## as a function of x and the speed.
 
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What is acceleration and how is it calculated?

Acceleration is the change in an object's velocity over time. It can be calculated by dividing the change in velocity by the time taken for that change to occur.

What is the difference between acceleration and velocity?

Velocity is the rate of change of an object's position over time, while acceleration is the rate of change of an object's velocity over time. In other words, velocity tells us how fast an object is moving, while acceleration tells us how that speed is changing.

How do we measure acceleration in real-world scenarios?

Acceleration can be measured using tools such as accelerometers, which can detect changes in an object's velocity. In addition, acceleration can be calculated using motion equations that take into account an object's initial velocity, final velocity, and time.

What is the role of acceleration in Newton's laws of motion?

Acceleration is a key concept in Newton's laws of motion. The first law states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction, which can result in acceleration.

What are some real-world examples of acceleration?

Some examples of acceleration in everyday life include a car speeding up or slowing down, a rollercoaster going around a loop, a person jumping off a diving board, or a ball being thrown into the air. In each of these scenarios, the object's velocity is changing, resulting in acceleration.

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