Why an object with constant acceleration cannot change its direction twice?

Question

Why an object with constant acceleration cannot change its direction twice?

Answer 1

Acceleration is a vector, so if it is constant, it is constant in magnitude and direction.

So, an object under constant acceleration, without any external force, cannot change direction, except in the trivial case of a reversal of direction.

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Answer 2

If an object has velocity -V (V>0) and acceleration a>0, clearly in come time, the velocity will become zero and change sign.  So the particle will change direction.  Now...

If you want the direction to change twice, the graph of position with time will be a cubic...s=f(t^3)

The derivative of the derivative (acceleration) is linear...that is the acceleration is changing in time (not constant).

-Fred

Answer 3

If an object is accelerating in one direction, and started out either at a standstill or already moving in the same direction as it's accelerating, it's obviously only going to continue to move in that direction faster and faster.

If an object moving left suddenly encounters a force moving right, then it will begin to accelerate right, although it will not instantly move right. First the force will slow it down from going left, then stop it, and then begin accelerating it right, at which point both the velocity and the accelerating are going in the same direction, and the object will continue accelerating ad infinitum.

Those are the only two outcomes, and only in one of them will it change direction, and even then it can only change direction once under constant acceleration.

Now, an object CAN change direction through acceleration, but not CONSTANT acceleration. If it is accelerating at an accelerating rate (IE for one minute it's going 1m/s faster every second and then the next minute it's going 2m/s faster every second), then it is possible for it to change direction twice.

Imagine throwing a toy rocket ship into the air with engines that took time to warm up, thus only applying a little force in the beginning but getting more and more powerful every second after starting. The rocket's thrusters will not be able to overcome gravity when they crank out very little force in the beginning, and thus when you throw the ship in the air it will begin to fall, changing direction. But before it hits the ground the thrusters will reach a point when they overcome gravity, thus allowing the ship to take off upwards. The ship changed direction twice, one to fall, and once to take off again. This was possible because it accelerated at an accelerating rate.