Question

why we called acceleration is equal to rate of change of velocity not speed why?

Answer 1

Answer:

The statement is \color{#D61F06}{\textbf{false}}false.

Explanation:

Acceleration is defined as the rate of change of velocity. Velocity is a vector, which means it contains a magnitude (a numerical value) and a direction. So the velocity can be changed either by changing the speed or by changing the direction of motion (or both). Therefore, it may be possible that the speed is constant, but the velocity is changing because the direction is changing. In this case, acceleration will be non-zero and equal to the rate of change of velocity.

It is a general misconception that rate of change of speed is equal to the magnitude of the rate of change of velocity. However, this is not true in all cases. Consider uniform circular motion: in the case of a uniform circular motion, the particle moves on a circular path with uniform speed. The speed remains constant, but the direction of motion is continuously changing. Due to change in direction of motion, acceleration is non-zero. This acceleration is toward the center of the circle and known as centripetal acceleration.

In general, acceleration can be resolved into two components. One component, which is parallel to the velocity, is known as tangential acceleration. This component changes the speed of the particle and is equal to the rate of change of speed. The other component of acceleration, which is perpendicular to velocity, is known as normal acceleration. This component is responsible for changing the direction of the velocity.

Velocity is the rate of change of displacement, while speed is the rate of change of distance. In other words, velocity is the rate of change of the shortest distance moved by a body from the final position to the initial position, while speed is the rate of change of the total length of the path traveled by a certain body.