Why when traveling a curved path does acceleration go inwards?

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SUMMARY

The discussion centers on the concept of acceleration in relation to curved motion. It is established that when an object travels along a curved path, its instantaneous acceleration points towards the concave side of the curve. This is due to the nature of acceleration being defined as the change in velocity, which occurs when an object alters its direction, even if its speed remains constant. The tangent line represents instantaneous velocity, while the inward acceleration reflects the change in direction of that velocity.

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proto3210
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Hello, I am having some trouble wrapping my mind around this concept. In the beginning of calculus I was taught that the derivative is relationship of change of one variable with respect to another variable, and that a good way to visualize this is the tangent of a curve at a point. My physics textbook notes that when traveling a curved path the instantaneous acceleration is pointed towards the concave side of the path. I do not quite understand why?

To find instantaneous velocity, even around a curved path it is the tangent line of the curve at a point. Why is acceleration different?
 
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Because acceleration is the change in velocity. How does the velocity change when you make a turn?
 

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