Acceleration is defined as the time derivative of velocity, represented mathematically as ##\vec a = d\vec v/dt##. In scenarios where speed remains constant, such as uniform circular motion, the velocity can be expressed as ##\vec v = v\vec e##, where ##\vec e## is a unit vector. The resulting acceleration is given by ##\vec a = v (d\vec e/dt)##, indicating that acceleration occurs due to changes in direction rather than speed. This phenomenon is exemplified by centripetal acceleration, which directs towards the center of the circular path.
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The most common example of this is uniform circular motion, where an object or particle moves in a circle at constant speed. In this case, the acceleration vector points to the centre of the circle. This is known as centripetal acceleration. See, for example:mancity said:Homework Statement: How would we define a value for acceleration if only the direction is changing and not the speed?
Relevant Equations: acceleration has both speed and direction
How would we define a value for acceleration if only the direction is changing and not the speed?