How can you say that an object is accelerate?

Answer 1

I don't know whether the question is asking "What happens to an accelerating object ?", or is asking "How can you tell whether the object is accelerated ?" So I'll try to address both aspects. Acceleration is defined as any change in the object's velocity vector ... magnitude, direction, or both. The magnitude of the vector is the part we usually think of when 'acceleration' is mentioned. Another word for the magnitude of the vector is the object's "speed". A change in speed is ceratainly acceleration, whether the speed is increasing or decreasing (negative acceleration). Change of speed is easily measured by observing the object's position at several points in time. The observer may be in a reference frame outside the object, or traveling with the object and measuring with respect to points in the external frame. (I'm not sure there's any difference.) But a change in speed is not a 'necessary' indication of acceleration. A change of direction is just as good. For example, consider a planet in circular orbit; or better, consider a geostationary 'TV' satellite. It's orbital 'speed' is virtually constant, yet it is in a situation of constant acceleration due to gravitation. The effect of the acceleration is the uniformly curved path. The direction of the velocity vector changes (with constant angular velocity), and the magnitude of the vector is constant. Change in the object's direction of motion may be even easier to observe from an external frame than a change in its speed. Simply get behind it and sight along its path. If the object ever departs from your line of sight, then it has acceleration.