Acceleration of an object is always directed perpendicular to its velocity

In summary, dropping two packages from the same height with 0 initial speed and acceleration due to gravity g will result in a constant distance between them if it does not depend on time. The distance between them can be found by subtracting their respective heights at any given time t. As for the second question, if the acceleration is always perpendicular to the velocity, then the object's speed will not increase as there is no component of acceleration in the same direction as the velocity. This results in the object moving in a circular motion with constant speed.
  • #1
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if i drop a package off a plane, then a second later i drop another package, the distance between the packages will be constant right? or would it be increasing? why?


if the acceleration of an object is always directed perpendicular to its velocity, is the object speeding up?
 
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  • #2
Taking the initial height to be H, acceleration due to gravity g, "drop" to mean initial speed is 0, and the moment you drop the first package to be t=0, its height at time t is given by
x1= (-g/2)t2+ H.

Dropping the second package at time t0> 0, from the same height with 0 initial speed, its height is given by
x2= (-g/2)(t-t0)2+ H.

The "distance between them" is x2- x1. That will be constant if it doesn't depend on t. Go ahead and do the algebra and see what happens.

As for your second question: assuming by "speed up", you mean "increase its speed"-i.e. the length of the velocity vector, changing the length of the velocity vector depends on the component of acceleration in the same direction as the velocity vector. In the case that the acceleration vector is perpendicular to the velocity vector, there is no parallel component.

In particular, if the acceleration is constant in magnitude (length of the vector) and perpendicular to the velocity vector, the motion is in a circle with constant speed.
 
  • #3


Yes, the object would be speeding up because acceleration is defined as any change in velocity, including a change in direction. In this scenario, the velocity of each package would be constantly increasing in the downward direction due to the force of gravity, which means the objects are accelerating. However, the distance between the packages would be increasing because they are both falling at different rates due to differences in their mass, air resistance, and other factors. So, the distance between the packages would be increasing, but the acceleration of each individual package remains perpendicular to its velocity.
 
  • #4


The object is not necessarily speeding up, as the acceleration and velocity are two separate factors. The acceleration may be directed perpendicular to the velocity, but it does not necessarily mean that the object is increasing in speed. It could also mean that the object is changing direction or experiencing a change in its velocity.

In the scenario of dropping packages off a plane, the distance between the packages would be increasing. This is because the packages are experiencing a constant downward acceleration due to gravity. This means that their velocity is increasing in the downward direction, which in turn causes the distance between them to increase over time.

To summarize, the acceleration of an object being directed perpendicular to its velocity does not determine whether the object is speeding up or not. In the scenario given, the distance between the packages would be increasing due to the constant acceleration of gravity acting on them.
 

FAQ: Acceleration of an object is always directed perpendicular to its velocity

1. What is acceleration?

Acceleration is the rate of change of an object's velocity over time. It is a vector quantity, meaning it has both magnitude and direction.

2. How is acceleration different from velocity?

Velocity is the rate of change of an object's displacement 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 and in what direction, while acceleration tells us how much an object's velocity is changing and in what direction.

3. Why is acceleration always directed perpendicular to an object's velocity?

This is because acceleration is the result of a force acting on an object. According to Newton's Second Law of Motion, the direction of acceleration is always in the same direction as the net force acting on the object. Since velocity and acceleration are perpendicular, it means that the force is acting at a right angle to the object's direction of motion.

4. Can an object accelerate without changing its velocity?

No, an object cannot accelerate without changing its velocity. This is because acceleration is defined as the rate of change of velocity, so a change in velocity is necessary for acceleration to occur.

5. How does acceleration affect an object's motion?

Acceleration affects an object's motion by changing its velocity. If an object is accelerating in a certain direction, it means that its velocity is increasing or decreasing in that direction. This will cause the object to either speed up, slow down, or change direction.

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