Why does velocity change when direction changes

For an object moving in a circle, this resultant force is the centripetal force that acts towards the middle of the circle. Gravitational attraction provides the centripetal force needed to keep a planet in orbit around the Sun, and a satellite in orbit around a planet.

For example, gravitational attraction between the Earth and the Moon keeps the Moon in orbit around the Earth. An object moving in a circular orbit at a constant speed has a changing velocity. That is, both the direction and the magnitude of the velocity vector are functions of time:. Using the rules for taking the derivative of a product, the acceleration vector is given by:.

In general though, the acceleration vector has two terms corresponding to the change in speed, and to the change in the direction of the velocity, respectively. The specific functional form of the acceleration vector will depend on the path being taken by the object. If we consider the case where speed is constant, then we have:. If the speed is constant, then the acceleration vector is given by:.

This means that the acceleration vector is perpendicular to the velocity vector if the speed is constant and the direction of the velocity changes. As a result of V y remaining fixed and V x continually changing, the velocity V of the body will continually change direction, coming to point more and more in the x direction.

You cannot achieve circular motion with a constant acceleration, as the direction of the acceleration must continually change to remain pointed at the centre as the body moves around the circumference. Not fully, no. The situation with uniform circular motion is actually slightly more complicated; this is a simpler case. I think what's confusing you is that you're thinking of the acceleration as of an intrinsic property, a vector attached to the body.

But acceleration is supplied by external forces. But that's just an extra complication. Any non-zero acceleration will by its nature affect the velocity of an object by "just existing" the acceleration doesn't need to "do" anything extra.

But let's ignore that for now. The math is more complicated with variable acceleration and involves integration, but the basic idea and the underlying logic is the same. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. The direction of the velocity of a body can change when its acceleration is constant. How is it possible since acceleration is a vector quantity? Ask Question. Asked 2 months ago. Active 1 month ago. Viewed 2k times. Is this case not similar to uniform circular motion? If not, please explain. Improve this question.