Will the acceleration increase or decrease with increase in velocity ?
Answers
Explanation:
Yes, it is possible for acceleration to decrease, while the velocity increases. Acceleration is the change of velocity with respect to time. Therefore, when the acceleration decreases, it means that the change of velocity is less, in other words, the velocity is increasing slower.
Let us first consider accelerated movements where acceleration has the same direction as velocity. In this case, acceleration, if positive, must decrease at some point. And as long as the acceleration is positive, the velocity increases. So (almost) all accelerated motions you can ever think of are examples to your question.
Cars, planes, bikes, runners, balls, rockets… Press your gas pedal any way you like, as long as you like, the acceleration must decrease at some point because nothing can accelerate forever. If it could, it could also travel at infinite velocity.
It is actually harder and more interesting to give the opposite example - one of a never-decreasing acceleration, or acceleration that does not start decreasing before the velocity has started decreasing. Until very recently it was impossible to name a single example for never-decreasing acceleration. Only in the past decade have we started regarding the expansion of the universe as continuously accelerating.
To give an example of (the intensity of the) acceleration (vector) that does not decrease before the (intensity of the) velocity (vector) has started decreasing, we have to consider cases where acceleration can be directed at an angle to the velocity. An example for this is the passage of two celestial bodies past each other, or orbiting each other. Both the acceleration and the velocity are at their peak at the closest point of the passage. And they both start decreasing at the same time just after this point - the velocity because the acceleration vector is now pointing at more than 90 degrees to the velocity vector, and the acceleration is decreasing because the distance between the bodies is increasing.
There are other examples as well, but all examples of acceleration decreasing at the same time or after the velocity starts decreasing involve more complex motion than the simple colinear acceleration, which always decreases before the velocity starts decreasing.