Acceleration of an object is always directed perpendicular to its velocity

[pringless]

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?

 

[HallsofIvy]

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.

 

[M98Ranger]

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.

 

[M98Ranger]

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.